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Riemannian Hypersurfaces with Constant Scalar Curvature In a Hessian Manifolds of Constant Curvature

Year 2009, Volume: 2 Issue: 2, 63 - 70, 30.10.2009

Münevver Y. Yılmaz , Mehmet Bektaş , Mahmut Ergüt

Abstract


Keywords

Hypersurface scalar curvature Hessian manifold

References

  • [1] Shima, H., Hessian manifolds of constant Hessian sectional curvature, J. Math. Soc. Japan, Vol 47, No.4, (1995), 735-753.
  • [2] Shima, H., Homogeneous Hessian manifolds, Ann. Inst. Fourier (Grenoble),30-3, (1980), 91-128.
  • [3] Shima, H., Vanishing theorems for compact Hessian manifolds, Ann. Inst. Fourier (Greno- ble),36-3, (1986), 183-205.
  • [4] Shima, H., Yagi, K., Geometry of Hessian manifolds, Diff. Geo. and Its Appl. 7 (1997), 277-290.
  • [5] Bektas, M, Yildirim, M., Kulahci, M., On hypersurfaces of Hessian manifolds with constant Hessian sectional curvature, Journal of Math. Statistics, 1 (2) ,(2005), 115-118.
  • [6] Bektas, M., Yildirim, M., Integral inequalities for submanifolds of Hessian Manifolds with constant Hessian sectional curvature, Iranian Journal of Sci. and Tech. Trans. A , Vol.30, No.A2, (2006), 235-239.
  • [7] Yildirim Yilmaz, M. Bektas, M., A survey on curvatures of Hessian manifolds, Chaos, Solitons and Fractals, vol.38, 3, (2008),620-630.
  • [8] Simons, J., Minimal variety in Riemannian manifolds, Ann. of Math. 88,(1968), 62-105.
  • [9] Chern, S. S., Do Cormo M., Kobayashi, S., Minimal submanifolds of a sphere with second fundamental form of constant length, Funct. Analysis and Related fields, Springer-Verlag, (1970),59-75.
  • [10] Nomizu, K., Smyth, B., A formula of Simons type and hypersurfaces with constant mean curvature, J. Diff. Geo. 3,(1969), 367-377.
  • [11] Nakagawa, H., Yokote, I., On hypersurfaces with constant scalar curvature in a Riemannian manifold of constant curvature, Kodai Math. Sem. Rep., 24, (1972), 471-481.
  • [12] Omachi, E., Hypersurfaces with harmonic curvature in a space of constant curvature, Kodai Math. J. 9, (1986), 170-174.

Year 2009, Volume: 2 Issue: 2, 63 - 70, 30.10.2009

Münevver Y. Yılmaz , Mehmet Bektaş , Mahmut Ergüt

Abstract

References

  • [1] Shima, H., Hessian manifolds of constant Hessian sectional curvature, J. Math. Soc. Japan, Vol 47, No.4, (1995), 735-753.
  • [2] Shima, H., Homogeneous Hessian manifolds, Ann. Inst. Fourier (Grenoble),30-3, (1980), 91-128.
  • [3] Shima, H., Vanishing theorems for compact Hessian manifolds, Ann. Inst. Fourier (Greno- ble),36-3, (1986), 183-205.
  • [4] Shima, H., Yagi, K., Geometry of Hessian manifolds, Diff. Geo. and Its Appl. 7 (1997), 277-290.
  • [5] Bektas, M, Yildirim, M., Kulahci, M., On hypersurfaces of Hessian manifolds with constant Hessian sectional curvature, Journal of Math. Statistics, 1 (2) ,(2005), 115-118.
  • [6] Bektas, M., Yildirim, M., Integral inequalities for submanifolds of Hessian Manifolds with constant Hessian sectional curvature, Iranian Journal of Sci. and Tech. Trans. A , Vol.30, No.A2, (2006), 235-239.
  • [7] Yildirim Yilmaz, M. Bektas, M., A survey on curvatures of Hessian manifolds, Chaos, Solitons and Fractals, vol.38, 3, (2008),620-630.
  • [8] Simons, J., Minimal variety in Riemannian manifolds, Ann. of Math. 88,(1968), 62-105.
  • [9] Chern, S. S., Do Cormo M., Kobayashi, S., Minimal submanifolds of a sphere with second fundamental form of constant length, Funct. Analysis and Related fields, Springer-Verlag, (1970),59-75.
  • [10] Nomizu, K., Smyth, B., A formula of Simons type and hypersurfaces with constant mean curvature, J. Diff. Geo. 3,(1969), 367-377.
  • [11] Nakagawa, H., Yokote, I., On hypersurfaces with constant scalar curvature in a Riemannian manifold of constant curvature, Kodai Math. Sem. Rep., 24, (1972), 471-481.
  • [12] Omachi, E., Hypersurfaces with harmonic curvature in a space of constant curvature, Kodai Math. J. 9, (1986), 170-174.
There are 12 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Münevver Y. Yılmaz

Mehmet Bektaş

Mahmut Ergüt This is me

Publication Date October 30, 2009
Published in Issue Year 2009 Volume: 2 Issue: 2

Cite

APA Y. Yılmaz, M., Bektaş, M., & Ergüt, M. (2009). Riemannian Hypersurfaces with Constant Scalar Curvature In a Hessian Manifolds of Constant Curvature. International Electronic Journal of Geometry, 2(2), 63-70.
AMA Y. Yılmaz M, Bektaş M, Ergüt M. Riemannian Hypersurfaces with Constant Scalar Curvature In a Hessian Manifolds of Constant Curvature. Int. Electron. J. Geom. October 2009;2(2):63-70.
Chicago Y. Yılmaz, Münevver, Mehmet Bektaş, and Mahmut Ergüt. “Riemannian Hypersurfaces With Constant Scalar Curvature In a Hessian Manifolds of Constant Curvature”. International Electronic Journal of Geometry 2, no. 2 (October 2009): 63-70.
EndNote Y. Yılmaz M, Bektaş M, Ergüt M (October 1, 2009) Riemannian Hypersurfaces with Constant Scalar Curvature In a Hessian Manifolds of Constant Curvature. International Electronic Journal of Geometry 2 2 63–70.
IEEE M. Y. Yılmaz, M. Bektaş, and M. Ergüt, “Riemannian Hypersurfaces with Constant Scalar Curvature In a Hessian Manifolds of Constant Curvature”, Int. Electron. J. Geom., vol. 2, no. 2, pp. 63–70, 2009.
ISNAD Y. Yılmaz, Münevver et al. “Riemannian Hypersurfaces With Constant Scalar Curvature In a Hessian Manifolds of Constant Curvature”. International Electronic Journal of Geometry 2/2 (October 2009), 63-70.
JAMA Y. Yılmaz M, Bektaş M, Ergüt M. Riemannian Hypersurfaces with Constant Scalar Curvature In a Hessian Manifolds of Constant Curvature. Int. Electron. J. Geom. 2009;2:63–70.
MLA Y. Yılmaz, Münevver et al. “Riemannian Hypersurfaces With Constant Scalar Curvature In a Hessian Manifolds of Constant Curvature”. International Electronic Journal of Geometry, vol. 2, no. 2, 2009, pp. 63-70.
Vancouver Y. Yılmaz M, Bektaş M, Ergüt M. Riemannian Hypersurfaces with Constant Scalar Curvature In a Hessian Manifolds of Constant Curvature. Int. Electron. J. Geom. 2009;2(2):63-70.