arXiv research

Spinor representation in isotropic space via Laguerre geometry.

Constructs a moment map flow for isotropic maps on surfaces.

Developed a new concept of isometric surfaces in isotropic space.

Study of invariant surfaces in isotropic and pseudo-isotropic geometries.

Study classifies zero mean curvature surfaces with planar curvature lines.

The study finds compact vacuum static spaces with positive isotropic curvature are spheres or products of a circle and sphere.

Study of surfaces in isotropic and pseudo-isotropic spaces using Gauss map and shape operator.

The paper studies hanging chains and surfaces in degenerate geometries.

This work extends holomorphic surface representations to isotropic space.

The paper develops RM frames for isotropic and pseudo-isotropic spaces and characterizes spherical curves.

The study examines surfaces in isotropic space with specific Gauss map properties.

The isotropic 3-space I^3 which is one of the Cayley--Klein spaces is obtained from the Euclidean space by substituting the usual Euclidean distance with the isotropic distance. In the present paper, we give several classifications on the surfaces in I^3 with the constant relative curvature (analogue of the Gaussian cu…

The paper finds formulas for special surface shapes in 3D space.

Classifies hypersurfaces with constant isotropic curvature in space forms.

Study on translation hypersurfaces with constant curvature in 4D isotropic space.

Paper proves a theorem about constant mean curvature surfaces in isotropic 3-space.

Chevalley theorems extended to isotropic functions on matrix spaces.

Paper investigates reflection principles for zero mean curvature surfaces in isotropic 3-space.

In this paper, we study factorable surfaces in a 3-dimensional isotropic space. We classify such surfaces with constant isotropic Gaussian (K) and mean curvature (H). We provide a non-existence result related with the surfaces satisfying H/K=const. Several examples are also illustrated.

The paper classifies almost isotropic Kähler manifolds, proving their properties.

The study of Laguerre isotropic hypersurfaces with rigidity and isoparametric properties.

New framework for zero mean curvature surfaces in isotropic 3-space.

A semi-isotropic space is a real affine 3-space endowed with the non-degenerate metric dx^{2}-dy^{2}. The main purpose of this paper is to describe the surfaces of revolution in the semi-isotropic space that satisfy some equations in terms of the position vector and the Laplace operators with respect to the first and t…

In this paper, we study the rotational surfaces in the isotropic 3-space I^3. satisfying Weingarten conditions in terms of the relative curvature K (analogue of the Gaussian curvature) and the isotropic mean curvature H. In particular, we classify such surfaces of linear Weingarten type in I^3.

In this paper, we define some non-Riemannian curvature properties for Cartan spaces. We consider Cartan space with the m-th root metric. We prove that every m-th root Cartan space of isotropic Landsberg curvature, or isotropic mean Landsberg curvature, or isotropic mean Berwald curvature reduces to a Landsberg, weakly …

In this paper we will show that a Lagrangian, Lorentzian surface $M^2_1$ in a complex pseudo space form $\widetilde M^2_1 (4c)$ is pseudo-isotropic if and only if $M$ is minimal. Next we will obtain a complete classification of all Lagrangian, Lorentzian surfaces which are lightlike pseudo-isotropic but not pseudo-isot…

The paper classifies and finds surfaces with specific curvature in isotropic spaces.

Study physical work done by isotropic vector forces along isotropic curves.

Simon Brendle's result extended to manifolds with positive isotropic curvature of dimension at least nine.

Let $R^{n+1, n}$ be the vector space $R^{2n+1}$ equipped with the bilinear form $(X,Y)=X^t C_n Y$ of index $n$, where $C_n= \sum_{i=1}^{2n+1} (-1)^{n+i-1} e_{i, 2n+2-i}$. A smooth $γ: R\to R^{n+1,n}$ is {\it isotropic} if $γ, γ_x, \ldots, γ_x^{(2n)}$ are linearly independent and the span of $γ, \ldots, γ_x^{(n-1)}$ is …

Study isotropic solutions in smooth metric measure spaces with vacuum Einstein equations.

Study on Hamiltonian stationary cones with isotropic links in 5-dimensional complex space.

In this paper, we extend the notion of affine translation surfaces introduced by Liu and Yu (Proc. Japan Acad. Ser. A Math. Sci. 89, 111--113, 2013) in a Euclidean space R^{3} to higher dimensional ambient spaces. We provide that an affine translation hypersurface of constant Gauss-Kronocker curvature K_{0} in R^{n+1} …

In this paper we prove the path connectedness of the moduli spaces of metrics with positive isotropic curvature on certain compact four-dimensional manifolds.

The paper studies conformally flat cubic metrics with isotropic curvature, finding they must be Minkowski.

Study loxodromes and geodesics on rotational surfaces in pseudo-isotropic space.

In this paper, we deal with the linear Weingarten factorable surfaces in the isotropic 3-space I^{3} satisfying the relation aK+bH=c, where K is the relative curvature and H the isotropic mean curvature, a,b,cR. We obtain a complete classification for such surfaces in I^{3}. As a further study, we classify all graph su…

We study singularities of geodesics flows in two-dimensional generalized Finsler spaces (pseudo-Finsler spaces). Geodesics are defined as extremals of a certain auxiliary functional whose non-isotropic extremals coincide with extremals of the action functional. This allows to consider isotropic lines as (unparametrized…

The study proves properties of high-dimensional manifolds with positive isotropic curvature.

In this paper we construct the differential equations of the stream lines that characterize plasma regarded as a non-isotropic medium geometrized by a jet rheonomic time-invariant Berwald-Moor metric. Section 1 contains historical notes regarding the Plasma Physics and its geometrical description. Section 2 analyzes th…

It was shown by Ramanathan \cite{R} that any compact oriented non-simply-connected minimal surface in the three-dimensional round sphere admits at most a finite set of pairwise noncongruent minimal isometric immersions. Here we show that this result extends to isotropic surfaces in spheres of arbitrary dimension. The c…

A proposal is made for what could well be the most natural symmetrical Riemannian spaces which are homogeneous but not isotropic, i.e. of what could well be the most natural class of symmetrical spaces beyond the spaces of constant Riemannian curvature, that is, beyond the spaces which are homogeneous and isotropic, or…

The paper solves orbital integrals on Lorentzian symmetric spaces.

Constructs a Morse-Bott function on symplectic Grassmannians.

The paper classifies critical metrics on manifolds with positive isotropic curvature.

We prove that if $(M^n,g)$, $n \ge 4$, is a compact, orientable, locally irreducible Riemannian manifold with nonnegative isotropic curvature, then one of the following possibilities hold: (i) $M$ admits a metric with positive isotropic curvature (ii) $(M,g)$ is isometric to a locally symmetric space (iii) $(M,g)$ is K…

Derive new Euler-Ramanujan-type identities and infinite decompositions for zero mean curvature graphs in various spaces.

In the Friedmann Model of the universe, cosmologists assume that spacelike slices of the universe are Riemannian manifolds of constant sectional curvature. This assumption is justified via Schur's Theorem by stating that the spacelike universe is locally isotropic. Here we define a Riemannian manifold as almost locally…