A characterization of totally real statistical submanifolds in quaternion Kaehler-like statistical manifolds

2021 ◽  
Vol 116 (1) ◽  
Author(s):  
Mohamd Saleem Lone ◽  
Mehraj Ahmad Lone ◽  
Adela Mihai
Keyword(s):  
Statistical Manifolds ◽  
Totally Real

scholarly journals On totally real statistical submanifolds

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4473-4483
Author(s):  
Aliya Siddiqui ◽  
Mohammad Shahid
Keyword(s):  
Sectional Curvature ◽  
Holomorphic Sectional Curvature ◽  
Fundamental Properties ◽  
Statistical Manifolds ◽  
Totally Real

In the present paper, first we prove some results by using fundamental properties of totally real statistical submanifolds immersed into holomorphic statistical manifolds. Further, we obtain the generalizedWintgen inequality for Lagrangian statistical submanifolds of holomorphic statistical manifolds with constant holomorphic sectional curvature c. The paper finishes with some geometric consequences of obtained results.

scholarly journals Ricci Curvature for Warped Product Submanifolds of Sasakian Space Forms and Its Applications to Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-15 ◽  
Author(s):  
Fatemah Mofarreh ◽  
Akram Ali ◽  
Nadia Alluhaibi ◽  
Olga Belova
Keyword(s):  
Warped Product ◽  
Necessary Conditions ◽  
Beltrami Operator ◽  
Warping Function ◽  
First Eigenvalue ◽  
Order Ordinary Differential Equation ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
Totally Real

In the present paper, we establish a Chen–Ricci inequality for a C-totally real warped product submanifold M n of Sasakian space forms M 2 m + 1 ε . As Chen–Ricci inequality applications, we found the characterization of the base of the warped product M n via the first eigenvalue of Laplace–Beltrami operator defined on the warping function and a second-order ordinary differential equation. We find the necessary conditions for a base B of a C-totally real-warped product submanifold to be an isometric to the Euclidean sphere S p .

A Characterization of Totally Real Carleman Sets and an Application to Products of Stratified Totally Real Sets

2016 ◽  
Vol 118 (2) ◽  
pp. 285 ◽  
Author(s):  
Benedikt S. Magnusson ◽  
Erlend Fornæss Wold
Keyword(s):  
Entire Functions ◽  
Carleman Approximation ◽  
Totally Real

We give a characterization of stratified totally real sets that admit Carleman approximation by entire functions. As an application we show that the product of two stratified totally real Carleman sets is a Carleman set.

scholarly journals Totally real orbits in affine quotients of reductive groups

1995 ◽  
Vol 139 ◽  
pp. 87-92
Author(s):  
H. Azad ◽  
J. J. Loeb ◽  
M. N. Qureshi
Keyword(s):  
Closed Subgroup ◽  
Symmetric Spaces ◽  
Related Result ◽  
Reductive Groups ◽  
Critical Set ◽  
Symmetric Subgroup ◽  
Real Submanifold ◽  
Totally Real ◽  
Connected Lie Group

Let K be a compact connected Lie group and L a closed subgroup of K In [8] M. Lassalle proves that if K is semisimple and L is a symmetric subgroup of K then the holomorphy hull of any K-invariant domain in Kc/Lc contains K/L. In [1] there is a similar result if L contains a maximal torus of K. The main group theoretic ingredient there was the characterization of K/L as the unique totally real K-orbit in Kc/Lc. On the other hand, Patrizio and Wong construct in [9] special exhaustion functions on the complexification of symmetric spaces K/L of rank 1 and find that the minimum value of their exhaustions is always achieved on K/L. By a lemma of Harvey and Wells [6] one knows that the set where a strictly plurisubharmonic (briefly s.p.s.h) function achieves its minimum is totally real. There is a related result in [2, Lemma 1.3] which states that if φ is any differentiable function on a complex manifold M then the form ddcφ vanishes identically on any real submanifold N contained in the critical set of φ; in particular if φ is s.p.s.h then N must be totally real.

scholarly journals Inequalities for the Casorati Curvature of Totally Real Spacelike Submanifolds in Statistical Manifolds of Type Para-Kähler Space Forms

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1399
Author(s):  
Bang-Yen Chen ◽  
Simona Decu ◽  
Gabriel-Eduard Vîlcu
Keyword(s):  
Scalar Curvature ◽  
Space Form ◽  
Space Forms ◽  
Statistical Manifolds ◽  
Spacelike Submanifolds ◽  
Totally Real ◽  
Casorati Curvature

The purpose of this article is to establish some inequalities concerning the normalized δ-Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant) of totally real spacelike submanifolds in statistical manifolds of the type para-Kähler space form. Moreover, this study is focused on the equality cases in these inequalities. Some examples are also provided.

Some inequalities for statistical submanifolds of quaternion Kaehler-like statistical space forms

2019 ◽  
Vol 16 (08) ◽  
pp. 1950129 ◽  
Author(s):  
Mohd. Aquib
Keyword(s):  
Space Forms ◽  
Statistical Manifolds ◽  
Statistical Submanifold ◽  
Totally Real ◽  
Statistical Version ◽  
Chen Inequality ◽  
Statistical Space

Motivated by one of the problems proposed by [Vilcu and Vilcu, Statistical manifolds with almost quaternionic structures and quaternionic Kaehler-like statistical submersions, Entropy 17 (2015) 6213–6228] in this paper, we study the statistical submanifolds of quaternion Kaehler-like statistical space forms and provide an answer to the problem. Further, we derive the statistical version of Chen inequality for totally real statistical submanifold in such ambient.

INVARIANT AND ANTI-INVARIANT RIEMANNIAN MAPS TO KÄHLER MANIFOLDS

2010 ◽  
Vol 07 (03) ◽  
pp. 337-355 ◽  
Author(s):  
BAYRAM ṢAHIN
Keyword(s):  
Riemannian Manifolds ◽  
Decomposition Theorem ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds ◽  
Riemannian Map ◽  
Definition Of ◽  
Totally Real

As a generalization of isometric immersions and Riemannian submersions, Riemannian maps were introduced by Fischer [Riemannian maps between Riemannian manifolds, Contemp. Math.132 (1992) 331–366]. It is known that a real valued Riemannian map satisfies the eikonal equation which provides a bridge between physical optics and geometrical optics. In this paper, we introduce invariant and anti-invariant Riemannian maps between Riemannian manifolds and almost Hermitian manifolds as a generalization of invariant immersions and totally real immersions, respectively. Then we give examples, present a characterization and obtain a geometric characterization of harmonic invariant Riemannian maps in terms of the distributions which are involved in the definition of such maps. We also give a decomposition theorem by using the existence of invariant Riemannian maps to Kähler manifolds. Moreover, we study anti-invariant Riemannian maps, give examples and obtain a classification theorem for umbilical anti-invariant Riemannian maps.

scholarly journals Screen transversal cauchy Riemann lightlike submanifolds

Filomat ◽  
2020 ◽  
Vol 34 (5) ◽  
pp. 1581-1599
Author(s):  
Burçin Doḡan ◽  
Bayram Şahin ◽  
Erol Yaşar
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
New Class ◽  
Metric Connection ◽  
Cauchy Riemann ◽  
Lightlike Submanifolds ◽  
Totally Real ◽  
Lightlike Submanifold

We introduce a new class of lightlike submanifolds, namely, Screen Transversal Cauchy Riemann (STCR)-lightlike submanifolds, of indefinite K?hler manifolds. We show that this new class is an umbrella of screen transversal lightlike, screen transversal totally real lightlike and CR-lightlike submanifolds. We give a few examples of a STCR lightlike submanifold, investigate the integrability of various distributions, obtain a characterization of such lightlike submanifolds in a complex space form and find new conditions for the induced connection to be a metric connection. Moreover, we investigate the existence of totally umbilical (STCR)-lightlike submanifolds and minimal (STCR)-lightlike submanifolds. The paper also contains several examples.

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