Inequalities involving k-Chen invariants for submanifolds of Riemannian product manifolds

Mehmet Gülbahar; Mukut Mani Trıpathı; Erol Kılıç

doi:10.31801/cfsuasmas.430856

Araştırma Makalesi

Inequalities involving k-Chen invariants for submanifolds of Riemannian product manifolds

Yıl 2019, Cilt: 68 Sayı: 1, 466 - 483, 01.02.2019

Mehmet Gülbahar Mukut Mani Trıpathı Erol Kılıç

https://doi.org/10.31801/cfsuasmas.430856

Öz

An optimal inequality involving the scalar curvatures, the mean curvature and the k-Chen invariant is established for Riemannian submanifolds. Particular cases of this inequality is reported. Furthermore, this inequality is investigated on submanifolds, namely slant, F-invariant and F-anti invariant submanifolds of an almost constant curvature manifold.

Anahtar Kelimeler

Curvature, Riemannian submanifolds, almost constant curvature manifold

Kaynakça

Adati, T., Submanifolds of an almost product manifold, Kodai Math. J. (1981), 4, 327-343.
Atçeken, M., Slant submanifolds of a Riemannian product manifold, Acta Math. Sci. Ser. B. Engl. Ed. (2010), 30(1), 215-224.
Bejancu, A., CR submanifolds of a Kaehler manifold I., Proc. Amer. Math. Soc. (1978), 69(1), 135-142.
Chen, B.-Y., A Riemannian invariant and its applications to submanifold theory, Festschrift dedicated to Katsumi Nomizu on his 70th birthday (Leuven, 1994; Brussels, 1994), Results Math. (1995), 27(1-2), 17-26.
Chen, B.-Y., Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions, Glasgow Math. J. (1999), 41, 33-41.
Chen, B.-Y., Riemannian DNA, inequalities and their applications, Tamkang J. Sci. and Eng. (2000), 3, 123-130.
Chen, B.-Y., Riemannian submanifolds, in Handbook of Differential Geometry, Vol. I, eds. F. Dillen and L. Verstraelen, North Holland, Amsterdam, 2000, 187-418.
Chen, B.-Y., On Ricci curvature of isotropic and Langrangian submanifolds in complex space forms, Arch. Math. (Basel) (2000), 74, 154-160.
Chen, B.-Y., Some new obstructions to minimal and Lagrangian isometric immersions, Japan. J. Math. (N.S.) (2000), 26(1), 105-127.
Chen, B.-Y., Pseudo-Riemannian Geometry, δ-invariants and applications, World Scientific, 2011.
Gülbahar, M., Kılıc, E. and Saraçoglu Çelik S., Special proper pointwise slant surfaces of a locally product Riemannian manifold, Turk. J. Math. (2015), 39, 884-899.
Kılıç, E., Tripathi, M. M. and Gülbahar, M., Chen-Ricci inequalities for submanifolds of Riemannian and Kaehlerian product manifolds, Ann. Polon. Math. (2016), 116(1), 37-56.
Liu, X. and Shao, F.-M., Skew semi-invariant submanifolds of a locally product manifold, Portugal. Math. (1999), 56(3), 319-327.
Sahin, B., Slant submanfiolds of an almost product Riemannian manifold, J. Korean Math. Soc. (2006), 43(4), 717-732.
Singer, I. M. and Thorpe, J. A., The curvature of 4-dimensional Einstein spaces, Global Analysis, Princeton University Press, 355-365, 1969.
Tachibana, S., Some theorems on locally product Riemannian spaces, Tohoku Math. J. (1960), 12, 281-293.
Tripathi, M. M., Almost semi-invariant submanifolds of a parallel ε-framed metric manifold, Ganita (1997), 48(1) 57-70. Yano, K., Differential geometry on complex and almost complex spaces, International Series of Monographs in Pure and Applied Mathematics 49. A Pergamon Press Book. The Macmillan Co., New York, 1965.
Yano, K., and Kon, M., Submanifolds of Kaehlerian product manifolds, Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. Ia. (1979), 15(5), 267-292.
Yano, K. and Kon, M., Structures on manifolds, Series in Pure Mathematics, World Scientific Publishing Co., Singapore, 1984.

Yıl 2019, Cilt: 68 Sayı: 1, 466 - 483, 01.02.2019

Mehmet Gülbahar Mukut Mani Trıpathı Erol Kılıç

https://doi.org/10.31801/cfsuasmas.430856

Öz

Kaynakça

Adati, T., Submanifolds of an almost product manifold, Kodai Math. J. (1981), 4, 327-343.
Atçeken, M., Slant submanifolds of a Riemannian product manifold, Acta Math. Sci. Ser. B. Engl. Ed. (2010), 30(1), 215-224.
Bejancu, A., CR submanifolds of a Kaehler manifold I., Proc. Amer. Math. Soc. (1978), 69(1), 135-142.
Chen, B.-Y., A Riemannian invariant and its applications to submanifold theory, Festschrift dedicated to Katsumi Nomizu on his 70th birthday (Leuven, 1994; Brussels, 1994), Results Math. (1995), 27(1-2), 17-26.
Chen, B.-Y., Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions, Glasgow Math. J. (1999), 41, 33-41.
Chen, B.-Y., Riemannian DNA, inequalities and their applications, Tamkang J. Sci. and Eng. (2000), 3, 123-130.
Chen, B.-Y., Riemannian submanifolds, in Handbook of Differential Geometry, Vol. I, eds. F. Dillen and L. Verstraelen, North Holland, Amsterdam, 2000, 187-418.
Chen, B.-Y., On Ricci curvature of isotropic and Langrangian submanifolds in complex space forms, Arch. Math. (Basel) (2000), 74, 154-160.
Chen, B.-Y., Some new obstructions to minimal and Lagrangian isometric immersions, Japan. J. Math. (N.S.) (2000), 26(1), 105-127.
Chen, B.-Y., Pseudo-Riemannian Geometry, δ-invariants and applications, World Scientific, 2011.
Gülbahar, M., Kılıc, E. and Saraçoglu Çelik S., Special proper pointwise slant surfaces of a locally product Riemannian manifold, Turk. J. Math. (2015), 39, 884-899.
Kılıç, E., Tripathi, M. M. and Gülbahar, M., Chen-Ricci inequalities for submanifolds of Riemannian and Kaehlerian product manifolds, Ann. Polon. Math. (2016), 116(1), 37-56.
Liu, X. and Shao, F.-M., Skew semi-invariant submanifolds of a locally product manifold, Portugal. Math. (1999), 56(3), 319-327.
Sahin, B., Slant submanfiolds of an almost product Riemannian manifold, J. Korean Math. Soc. (2006), 43(4), 717-732.
Singer, I. M. and Thorpe, J. A., The curvature of 4-dimensional Einstein spaces, Global Analysis, Princeton University Press, 355-365, 1969.
Tachibana, S., Some theorems on locally product Riemannian spaces, Tohoku Math. J. (1960), 12, 281-293.
Tripathi, M. M., Almost semi-invariant submanifolds of a parallel ε-framed metric manifold, Ganita (1997), 48(1) 57-70. Yano, K., Differential geometry on complex and almost complex spaces, International Series of Monographs in Pure and Applied Mathematics 49. A Pergamon Press Book. The Macmillan Co., New York, 1965.
Yano, K., and Kon, M., Submanifolds of Kaehlerian product manifolds, Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. Ia. (1979), 15(5), 267-292.
Yano, K. and Kon, M., Structures on manifolds, Series in Pure Mathematics, World Scientific Publishing Co., Singapore, 1984.

Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Bölüm	Makaleler
Yazarlar	Mehmet Gülbahar 0000-0001-6950-7633 Mukut Mani Trıpathı 0000-0002-6113-039X Erol Kılıç 0000-0001-7536-0404
Yayımlanma Tarihi	1 Şubat 2019
Gönderilme Tarihi	10 Ekim 2017
Kabul Tarihi	20 Şubat 2018
Yayımlandığı Sayı	Yıl 2019 Cilt: 68 Sayı: 1

Kaynak Göster

APA	Gülbahar, M., Trıpathı, M. M., & Kılıç, E. (2019). Inequalities involving k-Chen invariants for submanifolds of Riemannian product manifolds. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 466-483. https://doi.org/10.31801/cfsuasmas.430856
AMA	Gülbahar M, Trıpathı MM, Kılıç E. Inequalities involving k-Chen invariants for submanifolds of Riemannian product manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Şubat 2019;68(1):466-483. doi:10.31801/cfsuasmas.430856
Chicago	Gülbahar, Mehmet, Mukut Mani Trıpathı, ve Erol Kılıç. “Inequalities Involving K-Chen Invariants for Submanifolds of Riemannian Product Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, sy. 1 (Şubat 2019): 466-83. https://doi.org/10.31801/cfsuasmas.430856.
EndNote	Gülbahar M, Trıpathı MM, Kılıç E (01 Şubat 2019) Inequalities involving k-Chen invariants for submanifolds of Riemannian product manifolds. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 466–483.
IEEE	M. Gülbahar, M. M. Trıpathı, ve E. Kılıç, “Inequalities involving k-Chen invariants for submanifolds of Riemannian product manifolds”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 68, sy. 1, ss. 466–483, 2019, doi: 10.31801/cfsuasmas.430856.
ISNAD	Gülbahar, Mehmet vd. “Inequalities Involving K-Chen Invariants for Submanifolds of Riemannian Product Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (Şubat 2019), 466-483. https://doi.org/10.31801/cfsuasmas.430856.
JAMA	Gülbahar M, Trıpathı MM, Kılıç E. Inequalities involving k-Chen invariants for submanifolds of Riemannian product manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:466–483.
MLA	Gülbahar, Mehmet vd. “Inequalities Involving K-Chen Invariants for Submanifolds of Riemannian Product Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 68, sy. 1, 2019, ss. 466-83, doi:10.31801/cfsuasmas.430856.
Vancouver	Gülbahar M, Trıpathı MM, Kılıç E. Inequalities involving k-Chen invariants for submanifolds of Riemannian product manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):466-83.