Research Article
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Year 2024, , 137 - 145, 23.04.2024
https://doi.org/10.36890/iejg.1374716

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).

Biconservative Riemannian Submanifolds in Minkowski 5-Space

Year 2024, , 137 - 145, 23.04.2024
https://doi.org/10.36890/iejg.1374716

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 $\mathbb{E}^5_1$.

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).
There are 14 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Research Article
Authors

Rüya Yeğin Şen 0000-0002-2642-1722

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

Cite

APA Yeğin Şen, R. (2024). Biconservative Riemannian Submanifolds in Minkowski 5-Space. International Electronic Journal of Geometry, 17(1), 137-145. https://doi.org/10.36890/iejg.1374716
AMA Yeğin Şen R. Biconservative Riemannian Submanifolds in Minkowski 5-Space. Int. Electron. J. Geom. April 2024;17(1):137-145. doi:10.36890/iejg.1374716
Chicago Yeğin Şen, Rüya. “Biconservative Riemannian Submanifolds in Minkowski 5-Space”. International Electronic Journal of Geometry 17, no. 1 (April 2024): 137-45. https://doi.org/10.36890/iejg.1374716.
EndNote Yeğin Şen R (April 1, 2024) Biconservative Riemannian Submanifolds in Minkowski 5-Space. International Electronic Journal of Geometry 17 1 137–145.
IEEE R. Yeğin Şen, “Biconservative Riemannian Submanifolds in Minkowski 5-Space”, Int. Electron. J. Geom., vol. 17, no. 1, pp. 137–145, 2024, doi: 10.36890/iejg.1374716.
ISNAD Yeğin Şen, Rüya. “Biconservative Riemannian Submanifolds in Minkowski 5-Space”. International Electronic Journal of Geometry 17/1 (April 2024), 137-145. https://doi.org/10.36890/iejg.1374716.
JAMA Yeğin Şen R. Biconservative Riemannian Submanifolds in Minkowski 5-Space. Int. Electron. J. Geom. 2024;17:137–145.
MLA Yeğin Şen, Rüya. “Biconservative Riemannian Submanifolds in Minkowski 5-Space”. International Electronic Journal of Geometry, vol. 17, no. 1, 2024, pp. 137-45, doi:10.36890/iejg.1374716.
Vancouver Yeğin Şen R. Biconservative Riemannian Submanifolds in Minkowski 5-Space. Int. Electron. J. Geom. 2024;17(1):137-45.