arXiv research

The paper studies half-lightlike submanifolds in Lorentzian manifolds with specific distributions.

We investigate half-lightlike submanifolds with planar normal sections of four dimensional pseudo Euclidean space. We obtain necessary and sufficient conditions for a half-lightlike submanifold of $R_{2}^{4}$ such that it has degenerate or non-degenerate planar normal sections.

Study on a new type of submanifolds in geometric spaces.

We derive total mean curvature integration formulae of a three co-dimensional foliation $\mathcal{F}^{n}$ on a screen integrable half-lightlike submanifold, $M^{n+1}$ in a semi-Riemannian manifold $\overline{M}^{n+3}$. We give generalized differential equations relating to mean curvatures of a totally umbilical half-li…

Study on umbilical submanifolds in specific geometric spaces.

We introduce higher order mean curvatures of screen almost conformal (SAC) half-lightlike submanifolds of indefinite contact manifolds, admitting a semi-symmetric non-metric connection, and use them to generalize some known results of [6]. Also, we derive a new set of integration formulae via the divergence of some spe…

This paper surveys parallel submanifolds in Riemannian and pseudo-Riemannian manifolds.

The study characterizes submanifolds in product spaces.

Researchers describe a specific type of submanifolds in Euclidean space.

The paper finds many infinite-dimensional weakly reflective PF submanifolds in Hilbert spaces.

We introduce the notions of pointwise almost h-slant submanifolds and pointwise almost h-semi-slant submanifolds as a generalization of slant submanifolds, pointwise slant submanifolds, semi-slant submanifolds, and pointwise semi-slant submanifolds. We have characterizations and investigate the integrability of distrib…

Study lightlike submanifolds in indefinite statistical manifolds, finding conditions and curvature expressions.

Develops methods for computing conformal invariants of submanifolds.

The paper introduces austere and arid submanifolds in Hilbert spaces.

Sphere theorems for submanifolds in Kähler and Sasaki spaces.

Study of CR-submanifolds in various Lorentzian manifolds.

Study attached submanifolds in solvmanifolds, generalizing symmetric space results.

Survey of recent austere submanifold results.

The paper derives Chen inequalities for statistical submanifolds in cosymplectic manifolds.

Study on null submanifolds in indefinite complex contact geometry.

Study on deforming calibrated submanifolds with boundary constraints.

Minimal real Kähler submanifolds in codimension 6 are holomorphic.

Study various submanifolds in quaternionic skew-Hermitian spaces.

An n-dimensional submanifold X of a projective space P^N (C) is called tangentially degenerate if the rank of its Gauss mapping γ: X ---> G (n, N) satisfies 0 < rank γ< n. The authors systematically study the geometry of tangentially degenerate submanifolds of a projective space $P^N (\mathbf{C})$. By means of the foca…

Proves Frankel theorem for generic submanifolds in Sasakian manifolds.

The paper normalizes Poisson saturation of coregular submanifolds.

The paper studies $λ$-submanifolds in Gauss spaces and proves theorems for complete proper ones.

Study on special null submanifolds in indefinite Sasakian manifolds.

In this paper, invariant submanifolds of a generalized Kenmotsu manifold are studied. Necessary and sufficient conditions are given on a submanifold of a generalized Kenmotsu manifold to be an invariant submanifold.In this case, we investigate further properties of invariant submanifolds of \ a generalized Kenmotsu man…

Study on submanifolds of Euclidean space, classifying their symmetry types.

Constructs biharmonic and $r$-harmonic submanifolds in cohomogeneity one manifolds.

The paper studies a new type of submanifolds in product spaces.

Recent developments on biconservative submanifolds in Riemannian geometry.

Diffeological submanifolds are a new type of submanifold in manifold theory.

In this paper we study slant submanifolds of Lorentzian almost contact manifolds. We have taken the submanifold as a space like and then defined the slant angle on a submanifold and thus we extended the results of A. Lotta (Slant submanifolds in contact geometry [8]) and M. A. Khan et. al. (Slant submanifolds of Lorent…

The focal submanifolds of isoparametric hypersurfaces in spheres are all minimal Willmore submanifolds, mostly being $\mathcal{A}$-manifolds in the sense of A.Gray but rarely Ricci-parallel (\cite{QTY},\cite{LY},\cite{TY3}). In this paper we study the geometry of the focal submanifolds via Simons formula. We show that …

Study submanifolds in hyperbolic space, focusing on their boundary and Laplace operator.

Classifies totally geodesic submanifolds in Hopf-Berger spheres.

The paper examines the geometry of specific submanifolds in flag manifolds.

Study of mean curvature flow in hyperkähler manifolds leading to complex Lagrangian submanifolds.

We introduce a new class of lightlike submanifolds, namely, Screen Transversal Cauchy Riemann (STCR)-lightlike submanifolds, of indefinite Kaehler 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…

Study on submanifolds with specific types of factors in Kaehler manifolds.

Classifies minimal submanifolds in complex hyperbolic spaces.

The notion of Lagrangian $H$-umbilical submanifolds was introduced by B. Y. Chen in 1997, and these submanifolds have appeared in several important problems in the study of Lagrangian submanifolds from the Riemannian geometric point of view. Recently, the author introduced the notion of tangentially biharmonic submanif…

Study finds rigid submanifolds in spacelike waves under specific conditions.

Study on CR-lightlike submanifolds in golden semi-Riemannian manifolds.

Study shows area-minimizing submanifolds are mostly rough, not smooth.

Paper defines new submanifolds in Kaehler manifolds.