Araştırma Makalesi
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Locally Product-like Statistical Manifolds and Their Hypersurfaces

Yıl 2023, Cilt: 16 Sayı: 2, 435 - 450, 29.10.2023

Esra Erkan Kazuhiko Takano Mehmet Gülbahar

https://doi.org/10.36890/iejg.1307467
Cited By: 1

Öz

In this paper, almost product-like Riemannian manifolds are investigated. Basic properties on tangential hypersurfaces of almost product-like Riemannian manifolds are obtained. Some examples of tangential hypersurfaces are presented. Some relations involving the Riemannian curvature tensor of a tangential hypersurface are computed.

Anahtar Kelimeler

Riemannian product manifold hypersurface statistical manifold curvature

Destekleyen Kurum

TÜBİTAK

Proje Numarası

122F326

Teşekkür

The first and third authors of this paper is supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) with project number 122F326.

Kaynakça

  • [1] Adachi, T., Kimura, M., Maeda, S.: Real hypersurfaces some of whose geodesics are plane curves in non flat complex space form. Tohoku Math. J. 57 (2), 223-230 (2005).
  • [2] Adati, T.: Submanifolds of an almost product Riemannian manifold. Kodai Math. J. 4 (2), 327-343 (1981).
  • [3] Akbari, H., Malek, F.: On the hypersurfaces of almost hermitian statistical manifolds. Bull. Iran. Math. Soc. 48, 2669–2684 (2022).
  • [4] Amari, S.: Differential-geometrical methods in statistics, Lecture Notes in Statistics. vol. 28. Springer-Verlag, New York (1985).
  • [5] Aytimur, H. B., Özgür, C.: Inequalities for submanifolds of Sasaki-like statistical manifolds. Turk. J. Math. 42 (6), 3149-3163 (2018).
  • [6] Blair, D. E., Ludden, G. D.: Hypersurfaces in almost contact manifolds. Tohoku Math. J. 21 (3), 354-362 (1969).
  • [7] Calin, O., Udriste, C.: Geometric modeling in probability and statistics. Springer, Berlin, Germany (2014).
  • [8] Chen, B.-Y.: Geometry of Submanifolds. Marcel Dekker, New York-Basel (1973).
  • [9] Chen, B.-Y., Maeda, S.: Hopf hypersurfaces with constant principal curvatures in complex projective or complex hyperbolic spaces. Tokyo J. Math. 24 (1), 133-152 (2001).
  • [10] Deshmukh, S., Sharfuddin, A., Husain, S.I.: Hypersurfaces of almost product manifolds. Tamkang J. Math. 10, 169-181 (1979).
  • [11] Efron, B.: Defining the curvature of a statistical problem (with applications to second order efficiency). Ann. Statist. 3, 1189–1242 (1975).
  • [12] Erken, I. K., Murathan, C., Yazla, A.: Almost cosympletic statistical manifolds. Quaest. Math. 43 (2), 265-282 (2020).
  • [13] Eum, S. S.: On complex hypersurface in normal almost contact spaces. Tensor N. S. 19, 45-50 (1968).
  • [14] Feng, W. U., Jiang, Y., Zhang, L.: Some results on statistical hypersurfaces of Sasakian statistical manifolds and holomorphic statistical manifolds.
  • Int. Electron. J. Geom. 14 (1), 46-58 (2021).
  • [15] Furuhata, H.: Hypersurfaces in statistical manifolds. Differ. Geom. Appl. 27 (3), 420-429 (2009).
  • [16] Furuhata, H.: Statistical hypersurfaces in the space of Hessian curvature zero. Differ. Geom. Appl. 29 Suppl.1, S86-S90 (2011).
  • [17] Furuhata, H., Hasegawa, I.: Submanifold theory in holomorphic statistical manifolds, in: S. Dragomir, M.H. Shahid, F.R. Al-Solamy (Eds.),Geometry of Cauchy-Riemann Submanifolds. Springer, Singapore, 179-215 (2016).
  • [18] Furuhata, H., Hu, N., Vrancken, L.: Statistical hypersurfaces in the space of Hessian curvature zero II. Pure and Applied DifferentialGeometry-PADGE 2012 In Memory of Franki Dillen, Shaker Verlag GmbH, Germany, 136-142 (2013).
  • [19] Gucht, J.V.D., Davelaar, J., Hendriks, L., Porth, O., Olivares, H., Mizuno, Y., Fromm, C.M., Falcke, H.: Deep Horizon; a machine learningnetwork that recovers accreting black hole parameters. Astronomy-Astrophysics 636, A94 (2020).
  • [20] Kon, M.: A characterization of totally η-umbilical real hypersurfaces and ruled hypersurfaces of a complex space form. Czech. Math. J. 58 (4),1279-1287 (2008).
  • [21] Murathan, C., ¸Sahin, B.: A study ofWintgen like inequality for submanifolds in statistical warped product manifolds. J. Geom. 109 (2), 1-18 (2018).
  • [22] Sato, I., Matsumoto, K.: On P-Sasakian manifolds satisfying certain conditions. Tensor, New Ser. 33, 173-178 (1979).
  • [23] Takano, K.: Statistical manifolds with almost contact structures and its statistical submersions. J. Geom. 85, 171-187 (2006).
  • [24] Takano, K.: Statistical manifolds with almost complex structures. Tensor, New Ser. 72 (3), 225-231 (2010).
  • [25] Vilcu, A.D., Vilcu, G.E.: Statistical manifolds with almost quaternionic structures and quaternionic Kähler-like statistical submersions. Entropy 17 (9), 6213-6228 (2015).
  • [26] Vilcu, G.-E.: Almost product structures on statistical manifolds and para-Kähler-like statistical submersions. Bull. Sci. Math. 171, 21 (2021).
  • [27] Vos, P.W.: Fundamental equations for statistical submanifolds with applications to the Bartlett correction. Ann. Inst. Statist. Math. 41 (3), 429–450 (1989).
  • [28] Yano, K., Kon, M.: Structures on manifolds. Ser. Pure Math. 3, World Scientific Publishing Co., Singapore (1984).

Lokal Çarpım benzeri İstatistiksel Manifoldlar ve Hiperyüzeyleri

Yıl 2023, Cilt: 16 Sayı: 2, 435 - 450, 29.10.2023

Esra Erkan Kazuhiko Takano Mehmet Gülbahar

https://doi.org/10.36890/iejg.1307467
Cited By: 1

Öz

Bu çalışmada, hemen hemen çarpım benzeri Riemann manifoldları araştırılmıştır. Hemen hemen çarpım benzeri Riemann manifoldlarının teğet hiperyüzeyleri üzerindeki temel özellikler elde edilmiştir. Teğet hiperyüzeylerin bazı örnekleri sunulmuştur. Bir teğet hiperyüzeyin Riemann eğrilik tensörünü içeren bazı bağıntılar hesaplanmıştır.

Anahtar Kelimeler

Riemann çarpım manifoldu hiperyüzey istatistiksel manifold eğrilik

Proje Numarası

122F326

Kaynakça

  • [1] Adachi, T., Kimura, M., Maeda, S.: Real hypersurfaces some of whose geodesics are plane curves in non flat complex space form. Tohoku Math. J. 57 (2), 223-230 (2005).
  • [2] Adati, T.: Submanifolds of an almost product Riemannian manifold. Kodai Math. J. 4 (2), 327-343 (1981).
  • [3] Akbari, H., Malek, F.: On the hypersurfaces of almost hermitian statistical manifolds. Bull. Iran. Math. Soc. 48, 2669–2684 (2022).
  • [4] Amari, S.: Differential-geometrical methods in statistics, Lecture Notes in Statistics. vol. 28. Springer-Verlag, New York (1985).
  • [5] Aytimur, H. B., Özgür, C.: Inequalities for submanifolds of Sasaki-like statistical manifolds. Turk. J. Math. 42 (6), 3149-3163 (2018).
  • [6] Blair, D. E., Ludden, G. D.: Hypersurfaces in almost contact manifolds. Tohoku Math. J. 21 (3), 354-362 (1969).
  • [7] Calin, O., Udriste, C.: Geometric modeling in probability and statistics. Springer, Berlin, Germany (2014).
  • [8] Chen, B.-Y.: Geometry of Submanifolds. Marcel Dekker, New York-Basel (1973).
  • [9] Chen, B.-Y., Maeda, S.: Hopf hypersurfaces with constant principal curvatures in complex projective or complex hyperbolic spaces. Tokyo J. Math. 24 (1), 133-152 (2001).
  • [10] Deshmukh, S., Sharfuddin, A., Husain, S.I.: Hypersurfaces of almost product manifolds. Tamkang J. Math. 10, 169-181 (1979).
  • [11] Efron, B.: Defining the curvature of a statistical problem (with applications to second order efficiency). Ann. Statist. 3, 1189–1242 (1975).
  • [12] Erken, I. K., Murathan, C., Yazla, A.: Almost cosympletic statistical manifolds. Quaest. Math. 43 (2), 265-282 (2020).
  • [13] Eum, S. S.: On complex hypersurface in normal almost contact spaces. Tensor N. S. 19, 45-50 (1968).
  • [14] Feng, W. U., Jiang, Y., Zhang, L.: Some results on statistical hypersurfaces of Sasakian statistical manifolds and holomorphic statistical manifolds.
  • Int. Electron. J. Geom. 14 (1), 46-58 (2021).
  • [15] Furuhata, H.: Hypersurfaces in statistical manifolds. Differ. Geom. Appl. 27 (3), 420-429 (2009).
  • [16] Furuhata, H.: Statistical hypersurfaces in the space of Hessian curvature zero. Differ. Geom. Appl. 29 Suppl.1, S86-S90 (2011).
  • [17] Furuhata, H., Hasegawa, I.: Submanifold theory in holomorphic statistical manifolds, in: S. Dragomir, M.H. Shahid, F.R. Al-Solamy (Eds.),Geometry of Cauchy-Riemann Submanifolds. Springer, Singapore, 179-215 (2016).
  • [18] Furuhata, H., Hu, N., Vrancken, L.: Statistical hypersurfaces in the space of Hessian curvature zero II. Pure and Applied DifferentialGeometry-PADGE 2012 In Memory of Franki Dillen, Shaker Verlag GmbH, Germany, 136-142 (2013).
  • [19] Gucht, J.V.D., Davelaar, J., Hendriks, L., Porth, O., Olivares, H., Mizuno, Y., Fromm, C.M., Falcke, H.: Deep Horizon; a machine learningnetwork that recovers accreting black hole parameters. Astronomy-Astrophysics 636, A94 (2020).
  • [20] Kon, M.: A characterization of totally η-umbilical real hypersurfaces and ruled hypersurfaces of a complex space form. Czech. Math. J. 58 (4),1279-1287 (2008).
  • [21] Murathan, C., ¸Sahin, B.: A study ofWintgen like inequality for submanifolds in statistical warped product manifolds. J. Geom. 109 (2), 1-18 (2018).
  • [22] Sato, I., Matsumoto, K.: On P-Sasakian manifolds satisfying certain conditions. Tensor, New Ser. 33, 173-178 (1979).
  • [23] Takano, K.: Statistical manifolds with almost contact structures and its statistical submersions. J. Geom. 85, 171-187 (2006).
  • [24] Takano, K.: Statistical manifolds with almost complex structures. Tensor, New Ser. 72 (3), 225-231 (2010).
  • [25] Vilcu, A.D., Vilcu, G.E.: Statistical manifolds with almost quaternionic structures and quaternionic Kähler-like statistical submersions. Entropy 17 (9), 6213-6228 (2015).
  • [26] Vilcu, G.-E.: Almost product structures on statistical manifolds and para-Kähler-like statistical submersions. Bull. Sci. Math. 171, 21 (2021).
  • [27] Vos, P.W.: Fundamental equations for statistical submanifolds with applications to the Bartlett correction. Ann. Inst. Statist. Math. 41 (3), 429–450 (1989).
  • [28] Yano, K., Kon, M.: Structures on manifolds. Ser. Pure Math. 3, World Scientific Publishing Co., Singapore (1984).
Toplam 29 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Esra Erkan 0000-0003-0456-6418

Kazuhiko Takano 0000-0002-5247-2531

Mehmet Gülbahar 0000-0001-6950-7633

Proje Numarası 122F326
Erken Görünüm Tarihi 4 Ekim 2023
Yayımlanma Tarihi 29 Ekim 2023
Kabul Tarihi 27 Eylül 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 16 Sayı: 2

Kaynak Göster

APA Erkan, E., Takano, K., & Gülbahar, M. (2023). Locally Product-like Statistical Manifolds and Their Hypersurfaces. International Electronic Journal of Geometry, 16(2), 435-450. https://doi.org/10.36890/iejg.1307467
AMA Erkan E, Takano K, Gülbahar M. Locally Product-like Statistical Manifolds and Their Hypersurfaces. Int. Electron. J. Geom. Ekim 2023;16(2):435-450. doi:10.36890/iejg.1307467
Chicago Erkan, Esra, Kazuhiko Takano, ve Mehmet Gülbahar. “Locally Product-Like Statistical Manifolds and Their Hypersurfaces”. International Electronic Journal of Geometry 16, sy. 2 (Ekim 2023): 435-50. https://doi.org/10.36890/iejg.1307467.
EndNote Erkan E, Takano K, Gülbahar M (01 Ekim 2023) Locally Product-like Statistical Manifolds and Their Hypersurfaces. International Electronic Journal of Geometry 16 2 435–450.
IEEE E. Erkan, K. Takano, ve M. Gülbahar, “Locally Product-like Statistical Manifolds and Their Hypersurfaces”, Int. Electron. J. Geom., c. 16, sy. 2, ss. 435–450, 2023, doi: 10.36890/iejg.1307467.
ISNAD Erkan, Esra vd. “Locally Product-Like Statistical Manifolds and Their Hypersurfaces”. International Electronic Journal of Geometry 16/2 (Ekim 2023), 435-450. https://doi.org/10.36890/iejg.1307467.
JAMA Erkan E, Takano K, Gülbahar M. Locally Product-like Statistical Manifolds and Their Hypersurfaces. Int. Electron. J. Geom. 2023;16:435–450.
MLA Erkan, Esra vd. “Locally Product-Like Statistical Manifolds and Their Hypersurfaces”. International Electronic Journal of Geometry, c. 16, sy. 2, 2023, ss. 435-50, doi:10.36890/iejg.1307467.
Vancouver Erkan E, Takano K, Gülbahar M. Locally Product-like Statistical Manifolds and Their Hypersurfaces. Int. Electron. J. Geom. 2023;16(2):435-50.

Cited By

Screen invariant lightlike hypersurfaces of almost product-like statistical manifolds and locally product-like statistical manifolds
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