Harmonic morphisms of warped product type from Einstein manifolds

2007 ◽  
Vol 88 (4) ◽  
pp. 368-377
Author(s):  
H. Azad ◽  
M. T. Mustafa
Keyword(s):  
Warped Product ◽  
Product Type ◽  
Harmonic Morphisms ◽  
Einstein Manifolds

scholarly journals A Note on the Characterization of Two-Dimensional Quasi-Einstein Manifolds

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2013
Author(s):  
Gabriel Bercu
Keyword(s):  
Constant Curvature ◽  
Riemannian Manifolds ◽  
Warped Product ◽  
Product Type ◽  
Two Dimensional ◽  
Einstein Manifolds ◽  
Local Coordinates ◽  
Elementary Methods

In this article, we aim to introduce new classes of two-dimensional quasi-Einstein pseudo-Riemannian manifolds with constant curvature. We also give a classification of 2D quasi-Einstein manifolds of warped product type working in local coordinates. All the results are obtained by elementary methods.

scholarly journals On some classes of mixed-super quasi-Einstein manifolds

2016 ◽  
Vol 8 (1) ◽  
pp. 32-52
Author(s):  
Santu Dey ◽  
Buddhadev Pal ◽  
Arindam Bhattacharyya
Keyword(s):  
Warped Product ◽  
Einstein Manifold ◽  
Warped Products ◽  
Einstein Manifolds

Abstract Quasi-Einstein manifold and generalized quasi-Einstein manifold are the generalizations of Einstein manifold. The purpose of this paper is to study the mixed super quasi-Einstein manifold which is also the generalizations of Einstein manifold satisfying some curvature conditions. We define both Riemannian and Lorentzian doubly warped product on this manifold. Finally, we study the completeness properties of doubly warped products on MS(QE)4 for both the Riemannian and Lorentzian cases.

scholarly journals On Bach flat warped product Einstein manifolds

2013 ◽  
Vol 265 (2) ◽  
pp. 313-326 ◽  
Author(s):  
Qiang Chen ◽  
Chenxu He
Keyword(s):  
Warped Product ◽  
Einstein Manifolds ◽  
Bach Flat

scholarly journals ON DECOMPOSABLE AND WARPED PRODUCT GENERALIZED QUASI EINSTEIN MANIFOLDS

2017 ◽  
pp. 1061
Author(s):  
Prajjwal Pal ◽  
Sahanous Mallick
Keyword(s):  
Warped Product ◽  
Einstein Manifolds

The object of the present paper is to study decomposable and warped productgeneralized quasi Einstein manifolds.

On generalized quasi-Einstein manifolds

2019 ◽  
Vol 10 (3) ◽  
pp. 193-202 ◽  
Author(s):  
Mir Ahmad Mirshafeazadeh ◽  
Behroz Bidabad
Keyword(s):  
Fourth Order ◽  
Weyl Tensor ◽  
Warped Product ◽  
Regular Point ◽  
Product Manifold ◽  
Einstein Manifolds ◽  
Warped Product Manifold ◽  
Divergence Free

Abstract We study generalized quasi-Einstein manifolds, or briefly, GQE manifolds. Here, we present relations between the Bach, Cotton and D tensors on GQE manifolds. Next, a 3-tensor E which measures the deviation of m-quasi-Einstein manifolds from GQE manifolds is introduced. Among others in dimension 3, it is shown that Bach-flatness implies locally conformally flatness. Furthermore, it is proved that, around a regular point of the fourth-order divergence free Weyl tensor, a GQE manifold is a locally warped product manifold with {(n-1)} -dimensional Einstein fibers in suitable cases.

A NOTE ON THE CLASSIFICATION OF NONCOMPACT QUASI-EINSTEIN MANIFOLDS WITH VANISHING CONDITION ON THE WEYL TENSOR

2021 ◽  
pp. 1-11
Author(s):  
H. BALTAZAR ◽  
M. MATOS NETO
Keyword(s):  
Fourth Order ◽  
Weyl Tensor ◽  
Warped Product ◽  
Einstein Manifold ◽  
Dimensional Manifold ◽  
Einstein Manifolds ◽  
Weyl Curvature ◽  
Nonnegative Ricci Curvature ◽  
Simply Connected

Abstract The aim of this paper is to study complete (noncompact) m-quasi-Einstein manifolds with λ=0 satisfying a fourth-order vanishing condition on the Weyl tensor and zero radial Weyl curvature. In this case, we are able to prove that an m-quasi-Einstein manifold (m>1) with λ=0 on a simply connected n-dimensional manifold(M n , g), (n ≥ 4), of nonnegative Ricci curvature and zero radial Weyl curvature must be a warped product with (n–1)–dimensional Einstein fiber, provided that M has fourth-order divergence-free Weyl tensor (i.e. div4W =0).

scholarly journals Warped product pointwise bi-slant submanifolds of trans-Sasakian manifold

2020 ◽  
Vol 29 (2) ◽  
pp. 171-182
Author(s):  
Pahan Sampa
Keyword(s):  
Warped Product ◽  
Sasakian Manifold ◽  
Ricci Soliton ◽  
Einstein Manifolds ◽  
Slant Submanifold ◽  
Contact Metric Manifold ◽  
Almost Contact Metric Manifold ◽  
Slant Submanifolds ◽  
Almost Contact Metric ◽  
In Trans

The purpose of this paper is to study pointwise bi-slant submanifolds of trans-Sasakian manifold. Firstly, we obtain a non-trivial example of a pointwise bi-slant submanifolds of an almost contact metric manifold. Next we provide some fundamental results, including a characterization for warped product pointwise bi-slant submanifolds in trans-Sasakian manifold. Then we establish that there does not exist warped product pointwise bi-slant submanifold of trans-Sasakian manifold \tilde{M} under some certain considerations. Next, we consider that M is a proper pointwise bi-slant submanifold of a trans-Sasakian manifold \tilde{M} with pointwise slant distrbutions \mathcal{D}_1\oplus<\xi> and \mathcal{D}_2, then using Hiepko’s Theorem, M becomes a locally warped product submanifold of the form M_1\times_fM_2, where M_1 and M_2 are pointwise slant submanifolds with the slant angles \theta_1 and \theta_2 respectively. Later, we show that pointwise bi-slant submanifolds of trans-Sasakian manifold become Einstein manifolds admitting Ricci soliton and gradient Ricci soliton under some certain conditions..

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