Complex and Contact Manifolds II

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 30 March 2024 | Viewed by 7294

Special Issue Editors

Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, 010014 Bucharest, Romania
Interests: differentiable manifolds; Riemannian manifolds; distinguished vector fields; Riemannian invariants; sectional curvature; complex manifolds; contact manifolds; affine manifolds; statistical manifolds; submanifold theory
Special Issues, Collections and Topics in MDPI journals
Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, Bd. Lacul Tei 122-124, 020396 Bucharest, Romania
Interests: (pseudo-)Riemannian manifolds; curvature invariants; complex manifolds; contact manifolds, submanifold theory; statistical manifolds
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The most studied differentiable manifolds are those endowed with certain endomorphisms of their tangent bundles: almost complex, almost product, almost contact, and almost paracontact manifolds, etc. Among complex manifolds, Kaehler manifolds play the most important role via their geometrical properties. Roughly speaking, contact manifolds are the odd-dimensional version of complex manifolds; in particular, Sasakian manifolds correspond to Kaehler manifolds. There are topological obstructions to the existence of Kaehler and Sasakian structures, respectively, on compact Riemannian manifolds.

The geometry of submanifolds in such manifolds is an important topic of research. Obstructions to the existence of special classes of submanifolds in complex and Sasakian manifolds were obtained in terms of their Riemannian curvature invariants.

The purpose of this Special Issue is to collect selected review works written by well-known researchers in the field, as well as new developments in the geometry of complex and contact manifolds or/and explore applications in other areas.

This Issue is a continuation of the previous successful Special Issue “Complex and Contact Manifolds”.

Prof. Dr. Ion Mihai
Dr.  Adela Mihai
Guest Editors

Manuscript Submission Information

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Keywords

  • complex manifolds
  • contact manifolds
  • Riemannian invariants
  • complex contact manifolds
  • submanifolds in complex and contact manifolds
  • holomorphic and Sasakian statistical manifolds

Published Papers (6 papers)

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Research

18 pages, 323 KiB  
Article
On the Geometry of Kobayashi–Nomizu Type and Yano Type Connections on the Tangent Bundle with Sasaki Metric
Mathematics 2023, 11(18), 3865; https://doi.org/10.3390/math11183865 - 10 Sep 2023
Viewed by 604
Abstract
In this paper, we address the study of the Kobayashi–Nomizu type and the Yano type connections on the tangent bundle TM equipped with the Sasaki metric. Then, we determine the curvature tensors of these connections. Moreover, we find conditions under which these [...] Read more.
In this paper, we address the study of the Kobayashi–Nomizu type and the Yano type connections on the tangent bundle TM equipped with the Sasaki metric. Then, we determine the curvature tensors of these connections. Moreover, we find conditions under which these connections are torsion-free, Codazzi, and statistical structures, respectively, with respect to the Sasaki metric. Finally, we introduce the mutual curvature tensor on a manifold. We investigate some of its properties; furthermore, we study mutual curvature tensors on a manifold equipped with the Kobayashi–Nomizu type and the Yano type connections. Full article
(This article belongs to the Special Issue Complex and Contact Manifolds II)
20 pages, 309 KiB  
Article
From Dual Connections to Almost Contact Structures
Mathematics 2022, 10(20), 3822; https://doi.org/10.3390/math10203822 - 16 Oct 2022
Viewed by 872
Abstract
A dualistic structure on a smooth Riemaniann manifold M is a triple (M,g,) with g a Riemaniann metric and ∇ an affine connection generally assumed to be torsionless. From g and ∇, dual connection * can [...] Read more.
A dualistic structure on a smooth Riemaniann manifold M is a triple (M,g,) with g a Riemaniann metric and ∇ an affine connection generally assumed to be torsionless. From g and ∇, dual connection * can be defined. In this work, we give conditions on the basis of this notion for a manifold to admit an almost contact structure and some related structures: almost contact metric, contact, contact metric, cosymplectic, and co-Kähler in the three-dimensional case. Full article
(This article belongs to the Special Issue Complex and Contact Manifolds II)
15 pages, 304 KiB  
Article
Casorati Inequalities for Spacelike Submanifolds in Sasaki-like Statistical Manifolds with Semi-Symmetric Metric Connection
Mathematics 2022, 10(19), 3509; https://doi.org/10.3390/math10193509 - 26 Sep 2022
Viewed by 739
Abstract
In this paper, we establish some inequalities between the normalized δ-Casorati curvatures and the scalar curvature (i.e., between extrinsic and intrinsic invariants) of spacelike statistical submanifolds in Sasaki-like statistical manifolds, endowed with a semi-symmetric metric connection. Moreover, we study the submanifolds satisfying [...] Read more.
In this paper, we establish some inequalities between the normalized δ-Casorati curvatures and the scalar curvature (i.e., between extrinsic and intrinsic invariants) of spacelike statistical submanifolds in Sasaki-like statistical manifolds, endowed with a semi-symmetric metric connection. Moreover, we study the submanifolds satisfying the equality cases of these inequalities. We also present an appropriate example. Full article
(This article belongs to the Special Issue Complex and Contact Manifolds II)
18 pages, 311 KiB  
Article
Main Curvatures Identities on Lightlike Hypersurfaces of Statistical Manifolds and Their Characterizations
Mathematics 2022, 10(13), 2290; https://doi.org/10.3390/math10132290 - 30 Jun 2022
Cited by 3 | Viewed by 1071
Abstract
In this study, some identities involving the Riemannian curvature invariants are presented on lightlike hypersurfaces of a statistical manifold in the Lorentzian settings. Several inequalities characterizing lightlike hypersurfaces are obtained. These inequalities are also investigated on lightlike hypersurfaces of Lorentzian statistical space forms. [...] Read more.
In this study, some identities involving the Riemannian curvature invariants are presented on lightlike hypersurfaces of a statistical manifold in the Lorentzian settings. Several inequalities characterizing lightlike hypersurfaces are obtained. These inequalities are also investigated on lightlike hypersurfaces of Lorentzian statistical space forms. Full article
(This article belongs to the Special Issue Complex and Contact Manifolds II)
18 pages, 330 KiB  
Article
Some Pinching Results for Bi-Slant Submanifolds in S-Space Forms
Mathematics 2022, 10(9), 1538; https://doi.org/10.3390/math10091538 - 03 May 2022
Viewed by 1031
Abstract
The objective of the present article is to prove two geometric inequalities for submanifolds in S-space forms. First, we establish inequalities for the generalized normalized δ-Casorati curvatures for bi-slant submanifolds in S-space forms and then we derive the generalized Wintgen [...] Read more.
The objective of the present article is to prove two geometric inequalities for submanifolds in S-space forms. First, we establish inequalities for the generalized normalized δ-Casorati curvatures for bi-slant submanifolds in S-space forms and then we derive the generalized Wintgen inequality for Legendrian and bi-slant submanifolds in the same ambient space. We also discuss the equality cases of the inequalities. Further, we provide some immediate geometric applications of the results. Finally, we construct some examples of slant and Legendrian submanifolds, respectively. Full article
(This article belongs to the Special Issue Complex and Contact Manifolds II)
13 pages, 289 KiB  
Article
Relations between Extrinsic and Intrinsic Invariants of Statistical Submanifolds in Sasaki-Like Statistical Manifolds
Mathematics 2021, 9(11), 1285; https://doi.org/10.3390/math9111285 - 03 Jun 2021
Cited by 5 | Viewed by 1893
Abstract
The Chen first inequality and a Chen inequality for the δ(2,2)-invariant on statistical submanifolds of Sasaki-like statistical manifolds, under a curvature condition, are obtained. Full article
(This article belongs to the Special Issue Complex and Contact Manifolds II)
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