arXiv research

Solves classical problem with Kähler-Einstein metrics in complex projective spaces.

Advances in molecular "omics'" technologies have motivated new methodology for the integration of multiple sources of high-content biomedical data. However, most statistical methods for integrating multiple data matrices only consider data shared vertically (one cohort on multiple platforms) or horizontally (different …

Given two points of a Generalized Robertson-Walker spacetime, the existence, multiplicity and causal character of geodesic connecting them is characterized. Conjugate points of such geodesics are related to conjugate points of geodesics on the fiber, and Morse-type relations are obtained. Applications to bidimensional …

Valence two Killing tensors in the Euclidean and Minkowski planes are classified under the action of the group which preserves the type of the corresponding Killing web. The classification is based on an analysis of the system of determining partial differential equations for the group invariants and is entirely algebr…

The field equation for a spin 1/2 massive charged particle propagating in spacetimes that are the direct product of 2-dimensional spaces is separated. Moreover, we use this result to attain the separability of the Dirac equation in some specific static black hole solutions whose horizons have topology $\mathbb{R}\times…

Several modern applications require the integration of multiple large data matrices that have shared rows and/or columns. For example, cancer studies that integrate multiple omics platforms across multiple types of cancer, pan-omics pan-cancer analysis, have extended our knowledge of molecular heterogenity beyond what …

Develops a deterministic method to approximate NSDEs for better uncertainty quantification.

Extends micro-price concept to RFQ markets for fair pricing.

The Links-Gould invariant of alternating links has log-concave coefficients.

A submanifold of a Riemannian manifold is called a parallel submanifold if its second fundamental form is parallel with respect to the van der Waerden-Bortolotti connection. From submanifold point of view, parallel submanifolds are the simplest Riemannian submanifolds next to totally geodesic ones. Parallel submanifold…

The study characterizes submanifolds in product spaces.

Researchers describe a specific type of submanifolds in Euclidean space.

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…

Develops methods for computing conformal invariants of submanifolds.

We study lightlike submanifolds of indefinite statistical manifolds. Contrary to the classical theory of submanifolds of statistical manifolds, lightlike submanifolds of indefinite statistical manifolds need not to be statistical submanifold. Therefore we obtain some conditions for a lightlike submanifold of indefinite…

Survey of recent austere submanifold results.

Study of CR-submanifolds in various Lorentzian manifolds.

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

Study attached submanifolds in solvmanifolds, generalizing symmetric space results.

Study on null submanifolds in indefinite complex contact geometry.

In this paper we propose two efficient techniques which allow one to compute the price of American basket options. In particular, we consider a basket of assets that follow a multi-dimensional Black-Scholes dynamics. The proposed techniques, called GPR Tree (GRP-Tree) and GPR Exact Integration (GPR-EI), are both based …

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.

Austere submanifolds and arid submanifolds constitute respectively two different classes of minimal submanifolds in finite dimensional Riemannian manifolds. In this paper we introduce these two notions into a class of proper Fredholm (PF) submanifolds in Hilbert spaces, discuss their relation and show examples of infin…

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.

Classifies minimal submanifolds in complex hyperbolic spaces.

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

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…

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.

Warped product manifolds have been studied for a long period of time. In contrast, the study of warped product submanifolds from extrinsic point of view was initiated by the first author around the beginning of this century in [7, 8]. Since then the study of warped product submanifolds has been investigated by many geo…

Desingularizes conically singular Cayley submanifolds.