arXiv research

Recently, B.-Y. Chen and O. J. Garay studied pointwise slant submanifolds of almost Hermitian manifolds. By using the notion of pointwise slant submanifolds, we investigate the geometry of pointwise semi-slant submanifolds and their warped products in Sasakian and cosymplectic manifolds. We prove that there exist no pr…

The purpose of this paper is to study pointwise pseudo-slant warped product submanifolds of a Kähler manifold $\widetilde{M}$. We derive the conditions of integrability and totally geodesic foliation for the distributions allied to the characterization of a pointwise pseudo-slant submanifold of $\widetilde{M}$. The nec…

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…

As a generalization of slant submanifolds and semi-slant submanifolds, we introduce the notions of pointwise slant submanifolds and pointwise semi-slant sunmanifolds of an almost contact metric manifold. We obtain a characterization at each notion, investigate the topological properties of pointwise slant submanifolds,…

Study properties of pointwise k-slant submanifolds in Kähler manifolds.

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

Introduces $k$-slant distributions and submanifolds in various geometric settings.

Study on slant submanifolds with new conditions and transitivity.

In this paper, we study rotational surfaces of elliptic, hyperbolic and parabolic type with pointwise 1-type Gauss map which have spacelike profile curve in four dimensional pseudo Euclidean space E4-2 and obtain some characterizations for these rotational surfaces to have pointwise 1-type Gauss map.

We study a class of Riemannian manifolds with respect to the covariant derivative of their curvature tensors. We introduce geometrically the class of directed Riemannian manifolds of pointwise constant relative sectional curvature and give a tensor characterization for such manifolds. We prove that all rotational hyper…

In this paper, we proved a compactness result about Riemannian manifolds with an arbitrary pointwisely pinched Ricci curvature tensor.

The paper studies geometric properties of a specific type of submanifolds in Kaehler manifolds.

In this paper, we study spacelike rotational surfaces which are called boost invariant surfaces in Minkowski 4-space E41. We give necessary and sufficient condition for flat spacelike rotational surface to have pointwise 1-type Gauss map. Also, we obtain a characterization for boost invariant marginally trapped surface…

In this paper we study general rotational surfaces in the 4- dimensional Euclidean space E4 and give a characterization of flat general rotation surface with pointwise 1-type Gauss map. Also, we show that a non-planar flat general rotation surface with pointwise 1-type Gauss map is a Lie group if and only if it is a Cl…

Study bounds derivatives of solutions to a specific equation on domains.

A marginally trapped surface in the four-dimensional Minkowski space is a spacelike surface whose mean curvature vector is lightlike at each point. In the present paper we find all marginally trapped surfaces with pointwise 1-type Gauss map. We prove that a marginally trapped surface is of pointwise 1-type Gauss map if…

Our goal in this paper is to develop an effective estimator of fractal dimension. We survey existing ideas in dimension estimation, with a focus on the currently popular method of Grassberger and Procaccia for the estimation of correlation dimension. There are two major difficulties in estimation based on this method. …

An affine hypersurface $M$ is said to admit a pointwise symmetry, if there exists a subgroup $G$ of ${\rm Aut}(T_p M)$ for all $p\in M$, which preserves (pointwise) the affine metric $h$, the difference tensor $K$ and the affine shape operator $S$. Here, we consider 3-dimensional indefinite affine hyperspheres, i.e. $S…

In dimension greater than four, we prove that if a Hermitian non-Kaehler manifold is of pointwise constant antiholomorphic sectional curvatures, then it is of constant sectional curvatures.

It is known that there exist no warped product semi-slant submanifolds in Kaehler manifolds \cite{Sahin}. Recently, Chen and Garay studied pointwise-slant submanifolds of almost Hermitian manifolds in \cite{CG} and obtained many new results for such submanifolds. In this paper, we first introduce pointwise semi-slant s…

It is proved that if an almost Kähler manifold of dimension greater or equal to 8 is of pointwise constant antiholomorphic sectional curvature, then it is a complex space form.

This paper, focusing on the growth rate of the measure, gives pointwise bounds of solutions of eigenvalue equations of the Laplace-Beltrami operator on noncompact Riemannian manifolds.

Study constructs scattering theory for massless Dirac field on Kerr spacetime.

An affine hypersurface is said to admit a pointwise symmetry, if there exists a subgroup of the automorphism group of the tangent space, which preserves (pointwise) the affine metric h, the difference tensor K and the affine shape operator S. In this paper, we deal with positive definite affine hypersurfaces of dimensi…

In the present article we study a special class of surfaces in the four-dimensional Euclidean space, which are one-parameter systems of meridians of the standard rotational hypersurface. They are called meridian surfaces. We show that a meridian surface has a harmonic Gauss map if and only if it is part of a plane. Fur…

In this work, we study some classes of rotational surfaces in the pseudo-Euclidean space $\mathbb{E}^4_t$ with profile curves lying in 2-dimensional planes. First, we determine all such surfaces in the Minkowski 4-space $\mathbb{E}^4_1$ with pointwise 1-type Gauss map of the first kind and second kind. Then, we obtain …

New formalization of curved spaces using pointwise affine spaces.

We study the following problem: given an Einstein metric on a manifold, characterize and study all Einstein metrics which are pointwise projective to the given one. By definition, two metrics are said to be pointwise projectively related if they have the same geodesics as point sets. This is closely related to Hilbert'…

The present paper deals with the study of warped product pointwise bi-slant submanifolds of Kenmotsu manifolds with an example. The characterization for such submanifold is also discussed. An inequality of such submanifold is obtained and its equality case is also considered.

In this article we obtain a classification of strictly locally convex affine hypersurfaces in A^{n+1} for which the geometrical structure is pointwise invariant under the group SO(n-1) represented by rotations around a fixed axis in the tangent space.

There is a conjecture that a complete Riemannian 3-manifold with bounded sectional curvature, and pointwise pinched nonnegative Ricci curvature, must be flat or compact. We show that this is true when the negative part (if any) of the sectional curvature decays quadratically.

Study properties of specific submanifolds in metallic Riemannian spaces.

In this note we prove the a pointwise ergodic theorem for functions taking values in a separable complete CAT(0)-space, analogous to Lindenstrauss' pointwise ergodic theorem for real-valued integrable functions on a probability space subject to a probability-preserving action of an amenable l.c.s.c. group, where in the…

Recently Y{ü}ksel et. al. \cite{SY} shows that there doesn't exist any proper semi-slant warped product submanifolds in a Lorentzian paracosymplectic manifold. In the present article, we first define and give preparatory lemmas for a new generalize class of semi-slant submanifolds called pointwise semi-slant submanifol…

Study bounds on self-shrinkers with bounded HA for applications.

The present paper develops two concepts of pointwise differentiability of higher order for arbitrary subsets of Euclidean space defined by comparing their distance functions to those of smooth submanifolds. Results include that differentials are Borel functions, higher order rectifiability of the set of differentiabili…

In this paper, we study general rotational surfaces in the 4- dimensional pseudo-Euclidean space E4-2 and obtain a characterization of flat general rotation surfaces with pointwise 1-type Gauss map in E4-2 and give an example of such surfaces.

The paper develops axioms for uniquely decomposing functions with real arguments.

The paper proves existence and uniqueness of slant immersions in complex space forms.

We prove rigidity of any properly immersed noncompact Lagrangian shrinker with single valued Lagrangian angle for Lagrangian mean curvature flows. Our pointwise approach also provides an ele- mentary proof to the known rigidity results for graphical and almost graphical shrinkers of mean curvature flows.

In this note, a gradient estimate for the complex Monge-Ampere equation is established. It differs from previous estimates of Yau, Hanani, Blocki, P. Guan, B. Guan - Q. Li in that it is pointwise, and depends only on the infimum of the solution instead of its $C^0$ norm.

In this paper, by the studying of the Gauss map, Laplacian operator, curvatures of surfaces in $\mathbb{R}_{1}^{3}$ and Bour's theorem, we are going to identify surfaces of revolution with pointwise 1-type Gauss map property in $3-$dimensional Minkowski space.

This paper introduces a new clustering technique, called {\em dimensional clustering}, which clusters each data point by its latent {\em pointwise dimension}, which is a measure of the dimensionality of the data set local to that point. Pointwise dimension is invariant under a broad class of transformations. As a resul…

A Lorentz surface in the four-dimensional pseudo-Euclidean space with neutral metric is called quasi-minimal if its mean curvature vector is lightlike at each point. In the present paper we obtain the complete classification of quasi-minimal Lorentz surfaces with pointwise 1-type Gauss map.

We prove pointwise bounds for $L^2$ eigenfunctions of the Laplace-Beltrami operator on locally symmetric spaces with $\mathbb{Q}$-rank one if the corresponding eigenvalues lie below the continuous part of the $L^2$ spectrum. Furthermore, we use these bounds in order to obtain some results concerning the $L^p$ spectrum.

Estimates mean curvature flow with geometric bounds.

The paper analyzes uncertainty quantification in sparse Gaussian process regression with a Brownian motion prior.

Study proves properties of compact Hermitian surfaces with specific curvature conditions.