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GENERALIZED CHEN INEQUALITY FOR CR-WARPED PRODUCTS OF LOCALLY CONFORMAL KAHLER MANIFOLDS
Gauree Shanker,Harmandeep Kaur,Ramandeep Kaur,Abdulqader Mustafa 호남수학회 2024 호남수학학술지 Vol.46 No.1
The purpose of the Nash embedding theorem was to take extrinsic help for studying the intrinsic Riemannian geometry. To realize this aim in actual practice there is a need for optimal relationships between the known intrinsic invariants and the main extrinsic invariants for Riemannian submanifolds. This paper aims to provide an optimal relationship for CR-warped product submanifolds of locally conformal Kahler manifolds.
CLAIRAUT POINTWISE SLANT RIEMANNIAN SUBMERSION FROM NEARLY KAHLER MANIFOLDS
Gauree Shanker,Ankit Yadav 호남수학회 2023 호남수학학술지 Vol.45 No.1
In the present article, we introduce pointwise slant Riemannian submersion from nearly K¨ahler manifold to Riemannian manifold. We established the conditions for fibers to be totally geodesic. We also find necessary and sufficient conditions for pointwise slant submersion φ to be a harmonic and totally geodesic. Further, we study clairaut pointwise slant Riemannian submersion from nearly K¨ahler manifold to Riemannian manifold. We derive the clairaut conditions for φ such that φ is a clairaut map. Finally, one example is constructed which demonstrates existence of clairaut pointwise slant submersion from nearly K¨ahler manifold to Riemannian manifold
A NOTE ON SEMI-SLANT LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE KENMOTSU MANIFOLD
( Ramandeep Kaur ),( Gauree Shanker ),( Ankit Yadav ),( Akram Ali ) 호남수학회 2021 호남수학학술지 Vol.43 No.1
In this paper, we study the geometry of semi-slant lightlike submanifolds of an indefinite Kenmotsu manifold. The integrability conditions of distributions D<sub>1</sub> ⊕ {V },D<sub>2</sub> ⊕ {V } and RadTM on semi-slant lightlike submanifolds of an indefinite Kenmotsu manifold are defined. Furthermore, we derive necessary and sufficient conditions for the above distributions to have totally geodesic foliations.
On the Characterization of Conformally Flat Weakly Einstein Finsler Metrics
Seema Jangir,Gauree Shanker 경북대학교 자연과학대학 수학과 2023 Kyungpook mathematical journal Vol.63 No.4
In this paper, we prove that every weakly Einstein slope metric, which is con formally flat on a manifold M of dimension n ≥ 3, is either a locally Minkowski metric or a Riemannian metric. We also prove the same result for conformally flat weakly Einstein Kropina metrics.