Contact CR $ \delta $-invariant: an optimal estimate for Sasakian statistical manifolds

Aliya Naaz Siddiqui; Meraj Ali Khan; Amira Ishan; Aliya Naaz Siddiqui; Meraj Ali Khan; Amira Ishan

doi:10.3934/math.20241416

AIMS Mathematics

2024, Volume 9, Issue 10: 29220-29234. doi: 10.3934/math.20241416

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Research article

Contact CR $ \delta $-invariant: an optimal estimate for Sasakian statistical manifolds

1.
Division of Mathematics, School of Basic Sciences, Galgotias University, Greater Noida, Uttar Pradesh 203201, India
2.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box-65892, Riyadh 11566, Saudi Arabia
3.
Department of Mathematics, College of Science, Taif University, Taif 21944, Saudi Arabia

Received: 21 August 2024 Revised: 27 September 2024 Accepted: 08 October 2024 Published: 15 October 2024
MSC : 53C05, 49K35, 62B10

Chen (1993) developed the theory of $ \delta $-invariants to establish novel necessary conditions for a Riemannian manifold to allow a minimal isometric immersion into Euclidean space. Later, Siddiqui et al. (2024) derived optimal inequalities involving the CR $ \delta $-invariant for a generic statistical submanifold in a holomorphic statistical manifold of constant holomorphic sectional curvature. In this work, we extend the study of such optimal inequality to the contact CR $ \delta $-invariant on contact CR-submanifolds in Sasakian statistical manifolds of constant $ \phi $-sectional curvature. This paper concludes with a summary and final remarks.
- statistical manifolds,
- geometric inequality,
- generic submanifolds,
- $ \delta $-invariant
Citation: Aliya Naaz Siddiqui, Meraj Ali Khan, Amira Ishan. Contact CR $ \delta $-invariant: an optimal estimate for Sasakian statistical manifolds[J]. AIMS Mathematics, 2024, 9(10): 29220-29234. doi: 10.3934/math.20241416

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Abstract

Chen (1993) developed the theory of $ \delta $-invariants to establish novel necessary conditions for a Riemannian manifold to allow a minimal isometric immersion into Euclidean space. Later, Siddiqui et al. (2024) derived optimal inequalities involving the CR $ \delta $-invariant for a generic statistical submanifold in a holomorphic statistical manifold of constant holomorphic sectional curvature. In this work, we extend the study of such optimal inequality to the contact CR $ \delta $-invariant on contact CR-submanifolds in Sasakian statistical manifolds of constant $ \phi $-sectional curvature. This paper concludes with a summary and final remarks.

References

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