A characterization for totally real submanifolds using self-adjoint differential operator

Mohd. Aquib; Amira A. Ishan; Meraj Ali Khan; Mohammad Hasan Shahid; Mohd. Aquib; Amira A. Ishan; Meraj Ali Khan; Mohammad Hasan Shahid

doi:10.3934/math.2022006

AIMS Mathematics

2022, Volume 7, Issue 1: 104-120. doi: 10.3934/math.2022006

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Research article

A characterization for totally real submanifolds using self-adjoint differential operator

1.
Department of Mathematics, Sri Venkateshwara College, University of Delhi, New Delhi 110021, India
2.
Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
3.
Department of Mathematics, University of tabuk, Tabuk, Kingdom of Saudi Arabia
4.
Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi 110025, India

Received: 29 August 2021 Accepted: 26 September 2021 Published: 30 September 2021
MSC : 53C05, 53C20, 53C40

In this article, we study totally real submanifolds in Kaehler product manifold with constant scalar curvature using self-adjoint differential operator $ \Box $. Under this setup, we obtain a characterization result. Moreover, we discuss $ \delta- $invariant properties of such submanifolds and get an obstruction result as an application of the inequality derived. The results in the article are supported by non-trivial examples.
- totally real submanifolds,
- self-adjoint differential operator,
- Kaehler product manifold,
- $ \delta- $invariant
Citation: Mohd. Aquib, Amira A. Ishan, Meraj Ali Khan, Mohammad Hasan Shahid. A characterization for totally real submanifolds using self-adjoint differential operator[J]. AIMS Mathematics, 2022, 7(1): 104-120. doi: 10.3934/math.2022006

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Abstract

In this article, we study totally real submanifolds in Kaehler product manifold with constant scalar curvature using self-adjoint differential operator $ \Box $. Under this setup, we obtain a characterization result. Moreover, we discuss $ \delta- $invariant properties of such submanifolds and get an obstruction result as an application of the inequality derived. The results in the article are supported by non-trivial examples.

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