Einstein constant for almost hyperbolic Hermitian manifold on the product of two Sasakian manifolds

AUTHOR AND
AFFILIATION

SUSHIL SHUKLA

KEYWORDS:

Einstein, Hermitian structure, Sasakian manifold

Issue Date:

August 2013

Pages:

ISSN:

2319-8044 (Online) – 2231-346X (Print)

Source:

Vol.25 – No.2

PDF

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DOI:

jusps-A

ABSTRACT:

In 1981, Tsukada worked on the isospectral problem with respect to the complex Laplacian for a two-parameter family of Hermitian structures on the Calabi-Eckmann manifold S2p+1×S2q+1 including the canonical one. In this paper, we define a two-parameter family of almost hyperbolic Hermitian structures on the product manifoldM = M × M’ of a (2p + 1)- dimensional Sasakian manifold M and a (2q + 1)-dimensional Sasakian manifold M’ similarly to the method used in11, and show that any almost hyperbolic Hermitian structure on M belonging to the two parameter family is integrable and again find necessary and sufficient conditionfor a hyperbolic Hermitian manifold in the family to be Einstein

Copy the following to cite this Article:

SUSHIL SHUKLA, “Einstein constant for almost hyperbolic Hermitian manifold on the product of two Sasakian manifolds”, Journal of Ultra Scientist of Physical Sciences, Volume 25, Issue 2, Page Number , 2016


Copy the following to cite this URL:

SUSHIL SHUKLA, “Einstein constant for almost hyperbolic Hermitian manifold on the product of two Sasakian manifolds”, Journal of Ultra Scientist of Physical Sciences, Volume 25, Issue 2, Page Number , 2016

Available from: http://www.ultrascientist.org/paper/242/


In 1981, Tsukada worked on the isospectral problem with respect to the complex Laplacian for a two-parameter family of Hermitian structures on the Calabi-Eckmann manifold S2p+1×S2q+1 including the canonical one. In this paper, we define a two-parameter family of almost hyperbolic Hermitian structures on the product manifoldM = M × M’ of a (2p + 1)- dimensional Sasakian manifold M and a (2q + 1)-dimensional Sasakian manifold M’ similarly to the method used in11, and show that any almost hyperbolic Hermitian structure on M belonging to the two parameter family is integrable and again find necessary and sufficient conditionfor a hyperbolic Hermitian manifold in the family to be Einstein