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Compact Totally Real Minimal Submanifolds in a Bochner-Kaehler Manifold

Year 2018, , 254 - 257, 20.12.2018
https://doi.org/10.32323/ujma.422271

Abstract

In this paper, we establish the following results: Let $M$ be an $% m-$dimensional compact totally real minimal submanifold immersed in a locally symmetric Bochner-Kaehler manifold $\tilde{M}$ with Ricci curvature bounded from below. Then either $M$ is a totally geodesic or \begin{equation*} \inf r\leq \frac{1}{2}\left( \frac{1}{2}m\left( m-1\right) \tilde{k}-\frac{1% }{3}\left( m+1\right) \tilde{c}\right), \end{equation*}% where $r$ is the scalar curvature of $M.$

References

  • [1] B. Y. Chen, Some topological obstructions to Bochner-Kaehler metrics and their applications, J. Dif. Geom., 13 (1978), 547-558.
  • [2] B. Y. Chen, K. Yano, Manifolds with vanishing Weyl or Bochner curvature tensor, J. Math. Soc. Japan, 27(1975), 106-112.
  • [3] B. Y. Chen, F. Dilen, Totally real bisectional curvature, Bochner-Kaehler and Einstein-Kaehler manifolds, Differential Geom. Appl., 10(1999), 145-154.
  • [4] S. T. Yau, Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math., 28 (1975), 201-228.
  • [5] C. S. Houh, Totally Real submanifolds in a Bochner-Kaehler Manifold, Tensor, 32 (1978), 293-296.
  • [6] K. Iwasaki, N. Ogitsu, On the mean curvature for Anti-holomorphic p-plane in Kaehlerian spaces, Tohoku Math. J., 27 (1975), 313-317.
  • [7] M. Bektas¸, Totally real submanifolds in a quaternion space form, Czech. Math. J., 54(129) (2004), 341-346.
  • [8] H. Sun, Totally real pseudo-umblical submanifolds of quaternion space form, Glasgow Math. J., 40 (1998), 109-115.
  • [9] L. Ximin, Totally real submanifolds in a complex projective space, Int. J. Math. Math. Sci., 22(1) (1999), 205-208.
Year 2018, , 254 - 257, 20.12.2018
https://doi.org/10.32323/ujma.422271

Abstract

References

  • [1] B. Y. Chen, Some topological obstructions to Bochner-Kaehler metrics and their applications, J. Dif. Geom., 13 (1978), 547-558.
  • [2] B. Y. Chen, K. Yano, Manifolds with vanishing Weyl or Bochner curvature tensor, J. Math. Soc. Japan, 27(1975), 106-112.
  • [3] B. Y. Chen, F. Dilen, Totally real bisectional curvature, Bochner-Kaehler and Einstein-Kaehler manifolds, Differential Geom. Appl., 10(1999), 145-154.
  • [4] S. T. Yau, Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math., 28 (1975), 201-228.
  • [5] C. S. Houh, Totally Real submanifolds in a Bochner-Kaehler Manifold, Tensor, 32 (1978), 293-296.
  • [6] K. Iwasaki, N. Ogitsu, On the mean curvature for Anti-holomorphic p-plane in Kaehlerian spaces, Tohoku Math. J., 27 (1975), 313-317.
  • [7] M. Bektas¸, Totally real submanifolds in a quaternion space form, Czech. Math. J., 54(129) (2004), 341-346.
  • [8] H. Sun, Totally real pseudo-umblical submanifolds of quaternion space form, Glasgow Math. J., 40 (1998), 109-115.
  • [9] L. Ximin, Totally real submanifolds in a complex projective space, Int. J. Math. Math. Sci., 22(1) (1999), 205-208.
There are 9 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Zühal Küçükarslan Yüzbaşı

Mehmet Bektaş This is me

Münevver Yıldırım Yılmaz

Publication Date December 20, 2018
Submission Date May 9, 2018
Acceptance Date July 16, 2018
Published in Issue Year 2018

Cite

APA Küçükarslan Yüzbaşı, Z., Bektaş, M., & Yıldırım Yılmaz, M. (2018). Compact Totally Real Minimal Submanifolds in a Bochner-Kaehler Manifold. Universal Journal of Mathematics and Applications, 1(4), 254-257. https://doi.org/10.32323/ujma.422271
AMA Küçükarslan Yüzbaşı Z, Bektaş M, Yıldırım Yılmaz M. Compact Totally Real Minimal Submanifolds in a Bochner-Kaehler Manifold. Univ. J. Math. Appl. December 2018;1(4):254-257. doi:10.32323/ujma.422271
Chicago Küçükarslan Yüzbaşı, Zühal, Mehmet Bektaş, and Münevver Yıldırım Yılmaz. “Compact Totally Real Minimal Submanifolds in a Bochner-Kaehler Manifold”. Universal Journal of Mathematics and Applications 1, no. 4 (December 2018): 254-57. https://doi.org/10.32323/ujma.422271.
EndNote Küçükarslan Yüzbaşı Z, Bektaş M, Yıldırım Yılmaz M (December 1, 2018) Compact Totally Real Minimal Submanifolds in a Bochner-Kaehler Manifold. Universal Journal of Mathematics and Applications 1 4 254–257.
IEEE Z. Küçükarslan Yüzbaşı, M. Bektaş, and M. Yıldırım Yılmaz, “Compact Totally Real Minimal Submanifolds in a Bochner-Kaehler Manifold”, Univ. J. Math. Appl., vol. 1, no. 4, pp. 254–257, 2018, doi: 10.32323/ujma.422271.
ISNAD Küçükarslan Yüzbaşı, Zühal et al. “Compact Totally Real Minimal Submanifolds in a Bochner-Kaehler Manifold”. Universal Journal of Mathematics and Applications 1/4 (December 2018), 254-257. https://doi.org/10.32323/ujma.422271.
JAMA Küçükarslan Yüzbaşı Z, Bektaş M, Yıldırım Yılmaz M. Compact Totally Real Minimal Submanifolds in a Bochner-Kaehler Manifold. Univ. J. Math. Appl. 2018;1:254–257.
MLA Küçükarslan Yüzbaşı, Zühal et al. “Compact Totally Real Minimal Submanifolds in a Bochner-Kaehler Manifold”. Universal Journal of Mathematics and Applications, vol. 1, no. 4, 2018, pp. 254-7, doi:10.32323/ujma.422271.
Vancouver Küçükarslan Yüzbaşı Z, Bektaş M, Yıldırım Yılmaz M. Compact Totally Real Minimal Submanifolds in a Bochner-Kaehler Manifold. Univ. J. Math. Appl. 2018;1(4):254-7.

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