Abstract
Project Number
121F253
References
- [1] Caddeo, R., Montaldo, S., Oniciuc, C., Piu, P.: Surfaces in three- dimensional space forms with divergence-free stress-bienergy tensor. Ann. Mat. Pura Appl. (4) 193, no.2, 529-550 (2014).
- [2] Chen B.-Y.: Geometry of submanifolds. Marcel Dekker. New York (1973).
- [3] Chen B.-Y.: Pseudo-Riemannian Geometry, δ-invariants and Applications. Word Scientific. Hackensack (2011).
- [4] Chen B.-Y.: Chen’s Biharmonic Conjecture and Submanifolds with Parallel Normalized Mean Curvature Vector. Mathematics. 7(8), 710. (2019).
- [5] Fu Y.: On bi-conservative surfaces in Minkowski 3-space. J. Geometry Phys. 66, 71–79 (2013).
- [6] Jiang G. Y.: 2-harmonic maps and their first and second variational formulas. Chinese Ann. Math. Ser. A 7, 389–402 (1986).
- [7] Hasanis, T., Vlachos, I.: Hypersurfaces in E4 with harmonic mean curvature vector field. Math. Nachr. 172, 145-169 (1995).
- [8] Montaldo S., Oniciuc C., Ratto A.: Biconservative surfaces. J. Geom. Anal. 26, 313–329 (2016).
- [9] Nistor S.: Complete biconservative surfaces in R3 and S3. J. Geom. Phys. 110, 130-153 (2016).
- [10] Şen R., Turgay N. C.: Biharmonic PNMCV submanifolds in Euclidean 5-space. Turkish Journal of Mathematics. 47, 296-316 (2023).
- [11] Turgay, N. C.: H-hypersurfaces with 3 distinct principal curvatures in the Euclidean spaces. Ann. Mat. Pura Appl. 194, 1795–1807 (2015).
- [12] Turgay N.C., Upadhyay A.: Biconservative hypersurfaces in 4-dimensional Riemannian space forms. Math. Nachr. 292, 905 - 921 (2019).
- [13] Yeğin Şen R.: Biconservative Submanifolds with Parallel Normalized Mean Curvature Vector Field in Euclidean Spaces. Bull. Iran. Math. Soc. 48, 3185-3194 (2022).
- [14] Yeğin Şen R., Turgay N. C.: On biconservative surfaces in 4-dimensional Euclidean space. J. Math. Anal. Appl. 460, 565–581 (2018).
Abstract
In this study, we focus biconservative Riemannian submanifolds with parallel normalized mean curvature vector field (PNMCV) in $\mathbb{E}^5_1$. We obtain explicit classifications for these submanifolds with exactly two distinct principal curvatures of the shape operator along the mean curvature vector field. In particular, we investigate these submanifolds which have time-like and space-like mean curvature vector field in $\mathbb{E}^5_1$.
Keywords
Biconservative submanifolds submanifolds with parallel normalized mean curvature vector Minkowski space
Supporting Institution
TÜBİTAK
Project Number
121F253
Thanks
The author was supported by a 3501 project of the Scientific and Technological Research Council of Türkiye(TÜBİTAK) (Project Number:121F253)
References
- [1] Caddeo, R., Montaldo, S., Oniciuc, C., Piu, P.: Surfaces in three- dimensional space forms with divergence-free stress-bienergy tensor. Ann. Mat. Pura Appl. (4) 193, no.2, 529-550 (2014).
- [2] Chen B.-Y.: Geometry of submanifolds. Marcel Dekker. New York (1973).
- [3] Chen B.-Y.: Pseudo-Riemannian Geometry, δ-invariants and Applications. Word Scientific. Hackensack (2011).
- [4] Chen B.-Y.: Chen’s Biharmonic Conjecture and Submanifolds with Parallel Normalized Mean Curvature Vector. Mathematics. 7(8), 710. (2019).
- [5] Fu Y.: On bi-conservative surfaces in Minkowski 3-space. J. Geometry Phys. 66, 71–79 (2013).
- [6] Jiang G. Y.: 2-harmonic maps and their first and second variational formulas. Chinese Ann. Math. Ser. A 7, 389–402 (1986).
- [7] Hasanis, T., Vlachos, I.: Hypersurfaces in E4 with harmonic mean curvature vector field. Math. Nachr. 172, 145-169 (1995).
- [8] Montaldo S., Oniciuc C., Ratto A.: Biconservative surfaces. J. Geom. Anal. 26, 313–329 (2016).
- [9] Nistor S.: Complete biconservative surfaces in R3 and S3. J. Geom. Phys. 110, 130-153 (2016).
- [10] Şen R., Turgay N. C.: Biharmonic PNMCV submanifolds in Euclidean 5-space. Turkish Journal of Mathematics. 47, 296-316 (2023).
- [11] Turgay, N. C.: H-hypersurfaces with 3 distinct principal curvatures in the Euclidean spaces. Ann. Mat. Pura Appl. 194, 1795–1807 (2015).
- [12] Turgay N.C., Upadhyay A.: Biconservative hypersurfaces in 4-dimensional Riemannian space forms. Math. Nachr. 292, 905 - 921 (2019).
- [13] Yeğin Şen R.: Biconservative Submanifolds with Parallel Normalized Mean Curvature Vector Field in Euclidean Spaces. Bull. Iran. Math. Soc. 48, 3185-3194 (2022).
- [14] Yeğin Şen R., Turgay N. C.: On biconservative surfaces in 4-dimensional Euclidean space. J. Math. Anal. Appl. 460, 565–581 (2018).
Details
| Primary Language | English |
|---|---|
| Subjects | Algebraic and Differential Geometry |
| Journal Section | Research Article |
| Authors | |
| Project Number | 121F253 |
| Early Pub Date | April 5, 2024 |
| Publication Date | April 23, 2024 |
| Submission Date | October 11, 2023 |
| Acceptance Date | February 15, 2024 |
| Published in Issue | Year 2024 Volume: 17 Issue: 1 |
