arXiv research

We obtain a basic inequality involving the Laplacian of the warping function and the squared mean curvature of any warped product isometrically immersed in a Riemannian manifold without assuming any restriction on the Riemann curvature tensor of the ambient manifold. Applying this general theory, we obtain basic inequa…

Study on totally real submanifolds in $(LCS)_n$-manifolds.

Paper derives Chen's inequality for a specific type of submanifold in a generalized space form.

We present Chen-Ricci inequality and improved Chen-Ricci inequality for curvature like tensors. Applying our improved Chen-Ricci inequality we study Lagrangian and Kaehlerian slant submanifolds of complex space forms and C-totally real submanifolds of Sasakian space forms.

In this paper we establish a general inequality involving the Laplacian of the warping functions and the squared mean curvature of any doubly warped product isometrically immersed in a Riemannian manifold. Moreover, we obtain some geometric inequalities for C-totally real doubly warped product submanifolds of generaliz…

Paper constructs new minimal submanifolds in spheres by spinning given ones.

Minimal real Kähler submanifolds in codimension 6 are holomorphic.

Complex duality for real submanifolds in complex 3-manifolds.

Minimal totally real submanifolds in complex space forms have special umbilical properties.

The study finds Lagrangian submanifolds in adjoint semisimple orbits for real forms.

Geometric inequalities found for special submanifolds in complex space forms.

Paper establishes inequality for submanifolds in real space forms with semi-symmetric non-metric connection.

Study shows convergence for mean curvature flow on almost minimal totally real submanifolds.

In this article, we prove a Kahler extension theorem for real Kahler submanifolds of codimension 4 and rank at least 5. Our main theorem states that such a manifold is a holomorphic hypersurface in another real Kahler submanifold of codimension 2. This generalizes a result of Dajczer and Gromoll in 1997 which states th…

We study the normal holonomy group, i.e. the holonomy group of the normal connection, of a CR-submanifold of a complex space form. We complete the local classification of normal holonomies for complex submanifolds. We show that the normal holonomy group of a coisotropic submanifold acts as the holonomy representation o…

The study of real Einstein submanifolds in Kähler geometry.

Paper extends rigidity and vanishing results for totally real submanifolds under $L^p$-integrable conditions.

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

Study examines homology of contact CR-submanifolds in complex Euclidean space.

In 1991, Dajczer and Rodriguez proved in [10] that a complete minimal real Kahler submanifold of codimension 2, if with complex dimension > 2, would be either holomorphic, or a cylinder, or complex ruled. In this article, we generalize their result to real analytic complete real Kahler submanifolds of codimension 4. Th…

We prove the Lefchetz theorem for CR submanifolds in Hermitian symmetric spaces. As an application we prove the nonexistence of real analytic Levi flat submanifolds in such manifolds.

By using T. Oprea's optimization methods on submanifolds, we give another proof of the inequalities relating the normalized $δ-$Casorati curvature $\hatδ_c(n-1)$ for submanifolds in real space forms. Also, inequalities relating the normalized $δ-$Casorati curvature $δ_C(n-1)$ for submanifolds in real space forms are ob…

The thesis extends Riemannian submanifold theory to non-real settings, unifying various geometries.

The study improves Wintgen inequalities for submanifolds in specific geometric spaces.

Study $f$-minimal Lagrangian submanifolds in Kähler manifolds with real holomorphy potentials.

In Kaehler manifolds are investigated conformally flat totally real submanifolds, which are semiparallel or have semiparallel mean curvature vector.

The following results are proved: Theorem 1. A totally real semiparallel submanifold of constant curvature with parallel f-structure in the normal bundle of a Kähler manifold N is flat or a totally geodesic submanifold of N. Theorem 2. A totally real minimal semiparallel submanifold M with parallel f-structure in the n…

Roughly speaking, an ideal immersion of a Riemannian manifold into a real space form is an isometric immersion which produces the least possible amount of tension from the ambient space at each point of the submanifold. The main purpose of this paper is to completely classify all non-minimal ideal submanifolds of real …

The paper investigates conditions for compactness of submanifolds in Kahler manifolds.

Study on null submanifolds in indefinite complex contact geometry.

Hasse principle applied to area-minimizing submanifolds across different homology types.

Study on stabilities and moduli spaces of special affine Legendrian submanifolds.

Every closed, oriented, real analytic Riemannian 3-manifold can be isometrically embedded as a special Lagrangian submanifold of a Calabi-Yau 3-fold, even as the real locus of an antiholomorphic, isometric involution. Every closed, oriented, real analytic Riemannian 4-manifold whose bundle of self-dual 2-forms is trivi…

A local uniqueness property of holomorphic functions on real-analytic nowhere minimal CR submanifolds of higher codimension is investigated. A sufficient condition called almost minimality is given and studied. A weaker necessary condition, being contained a possibly singular real-analytic Levi-flat hypersurface is stu…

We give some results concerning the smoothness of the image of a real-analytic submanifold in complex space under the action of a finite holomorphic mapping. For instance, if the submanifold is not contained in a proper complex subvariety, we give a necessary and sufficient condition guaranteeing that its image is smoo…

Minimal submanifolds in matrix spaces proven for specific ranks.

New classification of spherical 2-Dupin submanifolds.

Examining singularities of commuting vector fields on submanifolds.

The paper classifies submanifolds in symmetric spaces without analyticity.

Classifies totally geodesic submanifolds and polar actions on Stiefel manifolds.

In this paper we study submanifolds of almost contact manifolds with Norden metric of codimension two with totally real normal spaces. Examples of such submanifolds as a Lie subgroups are constructed.

We construct a family of analytic discs attached to a real submanifold M \subset $\mathbb{C}^{N+1}$ of codimension $2$ defined near a CR singularity.

We prove that pseudo-holomorphic discs attached to a maximal totally real submanifold inherit their regularity from the regularity of the submanifold and of the almost complex structure. The proof is based on the computation of an explicit lower bound for the Kobayashi metric in almost complex manifolds, which also yie…

Classifies totally geodesic submanifolds in symmetric spaces.

The study describes the structure at infinity of submanifolds in real space forms.

It is proved that a germ of a real analytic CR map from a smooth real-analytic minimal CR manifold M to an essentially finite real-algebraic generic submanifold M' of P^N of the same CR-dimension extends as a holomorphic correspondence along M. Applications are given for pseudoconcave submanifolds of P^N.

We prove that every (compact) taut submanifold in Euclidean space is real algebraic, i.e., is a connected component of a real irreducible algebraic variety in the same ambient space. This answers affirmatively a question of Nicolaas Kuiper raised in the 1980s.

We construct biharmonic real hypersurfaces and Lagrangian submanifolds of Clifford torus type in $CP^n$ via the Hopf fibration; and get new examples of biharmonic submanifolds in $S^{2n+1}$ as byproducts .