A Study of Kahlerian Einstein Manifold with Bochner Curvature Tensor

P. Bhardwaj¹ , N. Kumar²

Section:Research Paper, Product Type: Journal-Paper
Vol.6 , Issue.4 , pp.89-92, Aug-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i4.8992

Online published on Aug 31, 2019

Copyright © P. Bhardwaj, N. Kumar . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
The main purpose of the present paper is to study of Kahlerian Einstein manifold with Bochner curvature tensor. Few interesting results for Kahlerian Einstein manifold with Bochner curvature tensor have been obtained. Further we discussed about the theory of Kahlerian Einstein manifold with Bochner curvature tensor with R is non-zero. If a non-affine holomorphically projective transformation satisfying the condition , .then Kahlerian manifold is terns into Kahlerian Einstein manifold. Necessary and sufficient condition that a holomorphically projective transformation is analytic in a Kahlerian Einstein manifold with non–vanishing scalar curvature tensor then its associated vector is analytic. An Kahlerian Einstein manifold, the associated vector of an analytic holomorphically projective transformation is analytic. An Einstein manifold with , any infinitesimal affine transformation is a killing vector. If the associated vector of an analytic holomorphically projective transformation satisfying the condition then a Kahlerian manifold satisfying the condition is not an Einstein manifold.

Key-Words / Index Term :
Kahlerian manifolds, Einstein manifold, Bochner Curvature Tensor, Kahlerian Einstein manifold, Killing vector, holomorphically projective transformation, Lie derivative, Lie Algebra, contravariant almost analytic vector, Covariant almost analytic vector

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