Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 

Saved Queries

Sign in to use this feature.

Search Filter Reset All

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
Add Subjects Reset
Select Subjects

Journals

remove_circle_outline
remove_circle_outline
remove_circle_outline
Add Journals Reset
Select Journals

Article Types

remove_circle_outline
Add Article Types Reset
Select Article Types

Countries / Regions

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
Add Countries / Regions Reset
Select Countries / Regions
Update Search
share announcement

Search Results (5)

Search Parameters:
Keywords = Bochner curvature tensor

Order results
Result details
Results per page
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
11 pages, 267 KB  
Article
On Bochner Flat Kähler B-Manifolds
by Cornelia-Livia Bejan, Galia Nakova and Adara M. Blaga
Axioms 2023, 12(4), 336; https://doi.org/10.3390/axioms12040336 - 30 Mar 2023
Cited by 2 | Viewed by 2286
Abstract
We obtain on a Kähler B-manifold (i.e., a Kähler manifold with a Norden metric) some corresponding results from the Kählerian and para-Kählerian context concerning the Bochner curvature. We prove that such a manifold is of constant totally real sectional curvatures if and only [...] Read more.
We obtain on a Kähler B-manifold (i.e., a Kähler manifold with a Norden metric) some corresponding results from the Kählerian and para-Kählerian context concerning the Bochner curvature. We prove that such a manifold is of constant totally real sectional curvatures if and only if it is a holomorphic Einstein, Bochner flat manifold. Moreover, we provide the necessary and sufficient conditions for a gradient Ricci soliton or a holomorphic η-Einstein Kähler manifold with a Norden metric to be Bochner flat. Finally, we show that a Kähler B-manifold is of quasi-constant totally real sectional curvatures if and only if it is a holomorphic η-Einstein, Bochner flat manifold. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application)
14 pages, 342 KB  
Article
Almost Riemann Solitons with Vertical Potential on Conformal Cosymplectic Contact Complex Riemannian Manifolds
by Mancho Manev
Symmetry 2023, 15(1), 104; https://doi.org/10.3390/sym15010104 - 30 Dec 2022
Cited by 2 | Viewed by 1961
Abstract
Almost-Riemann solitons are introduced and studied on an almost contact complex Riemannian manifold, i.e., an almost-contact B-metric manifold, which is obtained from a cosymplectic manifold of the considered type by means of a contact conformal transformation of the Reeb vector field, its dual [...] Read more.
Almost-Riemann solitons are introduced and studied on an almost contact complex Riemannian manifold, i.e., an almost-contact B-metric manifold, which is obtained from a cosymplectic manifold of the considered type by means of a contact conformal transformation of the Reeb vector field, its dual contact 1-form, the B-metric, and its associated B-metric. The potential of the studied soliton is assumed to be in the vertical distribution, i.e., it is collinear to the Reeb vector field. In this way, manifolds from the four main classes of the studied manifolds are obtained. The curvature properties of the resulting manifolds are derived. An explicit example of dimension five is constructed. The Bochner curvature tensor is used (for a dimension of at least seven) as a conformal invariant to obtain these properties and to construct an explicit example in relation to the obtained results. Full article
(This article belongs to the Special Issue Symmetry and Geometry in Physics II)
20 pages, 391 KB  
Article
On Singular Distributions With Statistical Structure
by Paul Popescu, Vladimir Rovenski and Sergey Stepanov
Mathematics 2020, 8(10), 1825; https://doi.org/10.3390/math8101825 - 17 Oct 2020
Cited by 1 | Viewed by 2368
Abstract
In this paper, we extend our previous study regarding a Riemannian manifold endowed with a singular (or regular) distribution, generalizing Bochner’s technique and a statistical structure. Following the construction of an almost Lie algebroid, we define the central concept of the paper: The [...] Read more.
In this paper, we extend our previous study regarding a Riemannian manifold endowed with a singular (or regular) distribution, generalizing Bochner’s technique and a statistical structure. Following the construction of an almost Lie algebroid, we define the central concept of the paper: The Weitzenböck type curvature operator on tensors, prove the Bochner–Weitzenböck type formula and obtain some vanishing results about the null space of the Hodge type Laplacian on a distribution. Full article
(This article belongs to the Special Issue Geometric Methods and their Applications)
18 pages, 357 KB  
Article
The Weitzenböck Type Curvature Operator for Singular Distributions
by Paul Popescu, Vladimir Rovenski and Sergey Stepanov
Mathematics 2020, 8(3), 365; https://doi.org/10.3390/math8030365 - 6 Mar 2020
Cited by 1 | Viewed by 2445
Abstract
We study geometry of a Riemannian manifold endowed with a singular (or regular) distribution, determined as an image of the tangent bundle under smooth endomorphisms. Following construction of an almost Lie algebroid on a vector bundle, we define the modified covariant and exterior [...] Read more.
We study geometry of a Riemannian manifold endowed with a singular (or regular) distribution, determined as an image of the tangent bundle under smooth endomorphisms. Following construction of an almost Lie algebroid on a vector bundle, we define the modified covariant and exterior derivatives and their L 2 adjoint operators on tensors. Then, we introduce the Weitzenböck type curvature operator on tensors, prove the Weitzenböck type decomposition formula, and derive the Bochner–Weitzenböck type formula. These allow us to obtain vanishing theorems about the null space of the Hodge type Laplacian. The assumptions used in the results are reasonable, as illustrated by examples with f-manifolds, including almost Hermitian and almost contact ones. Full article
(This article belongs to the Special Issue Geometric Structures and Interdisciplinary Applications)
11 pages, 237 KB  
Article
Pinching Theorems for a Vanishing C-Bochner Curvature Tensor
by Jae Won Lee and Chul Woo Lee
Mathematics 2018, 6(11), 231; https://doi.org/10.3390/math6110231 - 30 Oct 2018
Viewed by 2608
Abstract
The main purpose of this article is to construct inequalities between a main intrinsic invariant (the normalized scalar curvature) and an extrinsic invariant (the Casorati curvature) for some submanifolds in a Sasakian manifold with a zero C-Bochner tensor. Full article
(This article belongs to the Special Issue Differential Geometry)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying article 1-50 on page 1 of 1.
Back to TopTop