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Year 2017, Volume: 5 Issue: 1, 27 - 33, 30.04.2017

Münevver Yıldırım Yılmaz , Mehmet Bektaş

https://doi.org/10.36753/mathenot.421479
Cited By: 2

Abstract

References

  • [1] Shima, H. The Geometry of Hessian structures, World Scientific Publ., 2007.
  • [2] Shima, H., Homogeneous Hessian manifolds. Ann. Inst. Fourier, Grenoble,. 30, 3, (1980), 91-128.
  • [3] Shima, H., A differential geometric characterization of homogeneous sel-dual cones. Tsukuba J. Math Vol. 6, no.1, (1982), 79-88.
  • [4] Bektas, M., Yildirim, M., Integral inequalities for submanifolds of Hessian manifolds with constant Hessian sectional curvature. Iranian Journal of Sci. and Tech.Trans. A. Sci. vol.30, no.A2 (2006), 235-239.
  • [5] Yildirim Yilmaz,M., Bektas, M., A Survey on curvatures of Hessian manifolds. Chaos, Solitons and Fractals 38, (2008), 620-630.
  • [6] Hineva, S., Submanifolds for which a lower bound of the Ricci curvature is achieved. J.Geom. 88, (2008), 53-69.
  • [7] Cao,X.-F., Pseudo-umbilical submanifolds of constant curvature Riemannian manifolds, Glasgow Mathematical Journal vol.43,no. 1 (2001), 129-133.
  • [8] Yildirim Yilmaz, M. , Bektas, M. A Note on Pseudo-Umbilical Submanifolds of Hessian Manifolds with Constant Hessian Sectional Curvature International Scholarly Research Network ISRN Geometry Vol.2011, (2011), 1-12.

Curvature Inequalities between a Hessian Manifold with Constant Curvature and its Submanifolds

Year 2017, Volume: 5 Issue: 1, 27 - 33, 30.04.2017

Münevver Yıldırım Yılmaz , Mehmet Bektaş

https://doi.org/10.36753/mathenot.421479
Cited By: 2

Abstract

In this paper after a short description of Hessian manifolds, we establish new curvature inequalities
between a Hessian manifold and its submanifolds.

Keywords

Hessian Manifold Riemannian Curvature Tensor sectional curvature spaceform

References

  • [1] Shima, H. The Geometry of Hessian structures, World Scientific Publ., 2007.
  • [2] Shima, H., Homogeneous Hessian manifolds. Ann. Inst. Fourier, Grenoble,. 30, 3, (1980), 91-128.
  • [3] Shima, H., A differential geometric characterization of homogeneous sel-dual cones. Tsukuba J. Math Vol. 6, no.1, (1982), 79-88.
  • [4] Bektas, M., Yildirim, M., Integral inequalities for submanifolds of Hessian manifolds with constant Hessian sectional curvature. Iranian Journal of Sci. and Tech.Trans. A. Sci. vol.30, no.A2 (2006), 235-239.
  • [5] Yildirim Yilmaz,M., Bektas, M., A Survey on curvatures of Hessian manifolds. Chaos, Solitons and Fractals 38, (2008), 620-630.
  • [6] Hineva, S., Submanifolds for which a lower bound of the Ricci curvature is achieved. J.Geom. 88, (2008), 53-69.
  • [7] Cao,X.-F., Pseudo-umbilical submanifolds of constant curvature Riemannian manifolds, Glasgow Mathematical Journal vol.43,no. 1 (2001), 129-133.
  • [8] Yildirim Yilmaz, M. , Bektas, M. A Note on Pseudo-Umbilical Submanifolds of Hessian Manifolds with Constant Hessian Sectional Curvature International Scholarly Research Network ISRN Geometry Vol.2011, (2011), 1-12.
There are 8 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Münevver Yıldırım Yılmaz

Mehmet Bektaş

Publication Date April 30, 2017
Submission Date July 14, 2016
Published in Issue Year 2017 Volume: 5 Issue: 1

Cite

APA Yılmaz, M. Y., & Bektaş, M. (2017). Curvature Inequalities between a Hessian Manifold with Constant Curvature and its Submanifolds. Mathematical Sciences and Applications E-Notes, 5(1), 27-33. https://doi.org/10.36753/mathenot.421479
AMA Yılmaz MY, Bektaş M. Curvature Inequalities between a Hessian Manifold with Constant Curvature and its Submanifolds. Math. Sci. Appl. E-Notes. April 2017;5(1):27-33. doi:10.36753/mathenot.421479
Chicago Yılmaz, Münevver Yıldırım, and Mehmet Bektaş. “Curvature Inequalities Between a Hessian Manifold With Constant Curvature and Its Submanifolds”. Mathematical Sciences and Applications E-Notes 5, no. 1 (April 2017): 27-33. https://doi.org/10.36753/mathenot.421479.
EndNote Yılmaz MY, Bektaş M (April 1, 2017) Curvature Inequalities between a Hessian Manifold with Constant Curvature and its Submanifolds. Mathematical Sciences and Applications E-Notes 5 1 27–33.
IEEE M. Y. Yılmaz and M. Bektaş, “Curvature Inequalities between a Hessian Manifold with Constant Curvature and its Submanifolds”, Math. Sci. Appl. E-Notes, vol. 5, no. 1, pp. 27–33, 2017, doi: 10.36753/mathenot.421479.
ISNAD Yılmaz, Münevver Yıldırım - Bektaş, Mehmet. “Curvature Inequalities Between a Hessian Manifold With Constant Curvature and Its Submanifolds”. Mathematical Sciences and Applications E-Notes 5/1 (April 2017), 27-33. https://doi.org/10.36753/mathenot.421479.
JAMA Yılmaz MY, Bektaş M. Curvature Inequalities between a Hessian Manifold with Constant Curvature and its Submanifolds. Math. Sci. Appl. E-Notes. 2017;5:27–33.
MLA Yılmaz, Münevver Yıldırım and Mehmet Bektaş. “Curvature Inequalities Between a Hessian Manifold With Constant Curvature and Its Submanifolds”. Mathematical Sciences and Applications E-Notes, vol. 5, no. 1, 2017, pp. 27-33, doi:10.36753/mathenot.421479.
Vancouver Yılmaz MY, Bektaş M. Curvature Inequalities between a Hessian Manifold with Constant Curvature and its Submanifolds. Math. Sci. Appl. E-Notes. 2017;5(1):27-33.

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