arXiv research

Classifies contact metric spaces using hyperquadric bundles.

We show that non-degenerate hyperquadrics in R^{n+2} admit no skew branes. Stated more traditionally, a compact codimension-one immersed submanifold of a non-degenerate hyperquadric of euclidean space must have parallel tangent spaces at two distinct points. Similar results have been proven by others, but (except for e…

Study totally real flat minimal surfaces in hyperquadric.

The paper classifies 3D hypersurfaces with specific geometric properties.

The $n$-dimensional complex hyperquadric is a compact complex algebraic hypersurface defined by the quadratic equation in the $(n+1)$-dimensional complex projective space, which is isometric to the real Grassmann manifold of oriented 2- planes and is a compact Hermitian symmetric space of rank 2. In this paper we study…

Study minimal Lagrangian submanifolds of complex hyperquadric.

The paper studies minimal 2-spheres of constant curvature in complex hyperquadrics using matrix theory.

The paper studies the affine focal set of submanifolds in hypersurfaces, describing conditions for regularity and singularities.

Classifies CR-embedded 3-folds in 5D hyperquadrics using moving frames.

We introduce a new family of affine metrics on a locally strictly convex surface $M$ in affine 4-space. Then, we define the symmetric and antisymmetric equiaffine planes associated with each metric. We show that if $M$ is immersed in a locally strictly convex hyperquadric, then the symmetric and the antisymmetric plane…

Study of minimal immersions from a sphere to a complex hyperquadric.

A ${ m G}_2$-horospherical manifold is identified by its VMRT.

Study on triviality of tangent and generalized tangent bundles of manifolds.

Study on minimal two-spheres in complex hyperquadric, proving non-congruence of constant curvature spheres.

In this paper, we denone the generalized bicomplex numbers and give some algebraic properties of them. Also, we show that some hyperquadrics in R4 and R42 are Lie groups by using generalized bicomplex number product and obtain Lie algebras of these Lie groups. Morever, by using tensor product surfaces, we determine som…

We give series of explicit examples of Levi-nondegenerate real-analytic hypersurfaces in complex spaces that are not transversally holomorphically embeddable into hyperquadrics of any dimension. For this, we construct invariants attached to a given hypersurface that serve as obstructions to embeddability. We further st…

Study metallic structures on tangent bundles with lifts and integrability.

We classify compact Kähler manifolds with semi-positive holomorphic bisectional and big tangent bundles. We also classify compact complex surfaces with semi-positive tangent bundles and compact complex $3$-folds of the form $P(T^*X)$ whose tangent bundles are nef. Moreover, we show that if $X$ is a Fano manifold such t…

Study compact Kähler manifolds with pseudo-effective tangent bundles.

The article investigates conditions for isomorphism of singular tangent bundles.

Extends differential geometry concepts to manifolds with super tangent bundles.

Study on Ricci solitons on tangent and unit tangent bundles.

The paper defines a new structure on tangent sphere bundles and characterizes their properties.

This paper shows vector bundles and differential bundles are equivalent in smooth manifolds.

Researchers compute the cohomology of an elliptic tangent bundle.

The paper classifies surfaces with pseudo-effective tangent bundles.

Study geodesics and F-geodesics on tangent bundles over para-Kähler-Norden manifolds.

We propose a special deformation of the Sasaki metric on tangent and unit tangent bundle of a Hermitian locally symmetric manifold. Geodesics of this deformed metric have different projections on a base manifold for tangent or unit tangent bundle cases in contrast to usual Sasaki metric. Nevertheless, the projections o…

Higher-order tangent bundles have geometric structures compatible with their iterated bundle structure.

Characterizes special curves on surface tangent bundles.

Study on singularities of bundle homomorphisms induced by Morin maps.

Homogeneous Fano manifolds with specific bundle properties proven.

This paper develops differential bundles and fibrations in tangent categories.

Study positive characteristic Fano 4-folds with nef tangent bundles.

Researchers found all invariant contact structures on tangent sphere bundles of compact symmetric spaces.

We show, using two different approaches, that there exists a family of Riemannian metrics on the tangent bundle of a two-sphere, which induces metrics of constant curvature on its unit tangent bundle. In other words, given such a metric on the tangent bundle of a two-sphere, the Hopf map is identified with a Riemannian…

In this short article, we establish a rigidity theorem for pairs of hyperquadrics in a weaker sense, i.e., we impose a condition that minimal rational curves are preserved, which is stronger than inheriting a sub-VMRT structure, a notion raised by Mok & Zhang (2014). This problem has its source in a theorem of Tsai (19…

We consider hypersurfaces in the real Euclidean space $\mathbb{R}^{n+1}$ ($n\geq2$) which are relatively normalized. We give necessary and sufficient conditions a) for a surface of negative Gaussian curvature in $\mathbb{R}^3$ to be ruled, b) for a hypersurface of positive Gaussian curvature in $\mathbb{R}^{n+1}$ to be…

New metrics found on tangent bundles of Riemannian surfaces.

In this paper we study a Riemanian metric on the tangent bundle $T(M)$ of a Riemannian manifold $M$ which generalizes Sasaki metric and Cheeger Gromoll metric and a compatible almost complex structure which together with the metric confers to $T(M)$ a structure of locally conformal almost Kählerian manifold. This is th…

Study metallic structures on P-Sasakian manifolds.

We consider trivializations of second iterated bundles of a Lie group that preserve lifted group structures. With such a trivialization, we elaborate Hamiltonian dynamics on cotangent, Lagrangian dynamics on tangent bundles and, both Hamiltonian and Lagrangian dynamics on Tulczyjew's symplectic space which is tangent o…

Sprays on Frechet manifolds connect connections and tangent structures.

The paper studies geometric structures on tangent and sphere bundles over statistical manifolds.

Geometrizes time-dependent mechanics using second order tangent bundles.

Sasakian structures found on tangent sphere bundles of certain symmetric spaces.

Study shows some biquotients have non-biquotient tangent bundles.

Constructs Lie groupoid integrating elliptic tangent bundles and Poisson structures.