arXiv research

The paper studies new curvature properties in Finsler geometry.

Generalizations of the classical affine Lelieuvre formula to surfaces in projective three-dimensional space and to hypersurfaces in multi- dimensional projective space are given. A discrete version of the projective Lelieuvre formula is presented too.

Characterizes minor-minimal separating projective planar graphs and their generalizations.

Projective geometry aids in analyzing fields near compact manifolds.

The authors give a complete classification of projective threefolds admitting a holomorphic normal projective connection. Moreover, they prove a general structure theorem on complex projective manifolds admitting a holomorphic normal projective connection, saying in particular, that any such manifold is either the proj…

Characterizes projective special complex manifolds using c-projective structures.

The study classifies holomorphic projective connections on complex threefolds.

Killing tensors on complex projective space are identified and generated by Killing fields.

We introduce the notion of a ``projective hull'' for subsets of complex projective varieties, parallel to the idea of the polynomial hull in affine varieties. With this concept, a generalization of J. Wermer's classical theorem on the hull of a curve in $C^n$ is established in the projective setting. The projective hul…

Paper studies pseudo-projective tensors on warped products.

Study on unique generalized Gauss maps of minimal surfaces sharing hypersurfaces in projective varieties.

Paper introduces new Finsler metrics preserved under projective transformations.

No projective structure found on foliations of elliptic curves.

Projective structures are mostly rigid at the boundary but some are not.

We correct a mistake in Shen Yibing, Yu Yaoyong, On Projectively Related Randers Metrics, International Journal of Mathematics 19}(2008), no. 5, 503--520, and prove the natural generalization of the projective Lichnerowicz-Obata conjecture for Randers metrics.

Efficiently solves heterogeneous QPs by reducing variables using instance-specific projections.

Study surfaces with free product fundamental groups, proving existence and properties.

A classical result asserts that the complex projective plane modulo complex conjugation is the 4-dimensional sphere. We generalize this result in two directions by considering the projective planes over the normed real division algebras and by considering the complexifications of these four projective planes.

A real projective orbifold is an $n$-dimensional orbifold modeled on $\mathbb{RP}^n$ with the group $PGL(n+1, \mathbb{R})$. We concentrate on an orbifold that contains a compact codimension $0$ submanifold whose complement is a union of neighborhoods of ends, diffeomorphic to closed $(n-1)$-dimensional orbifolds times …

The paper explores properties of projections and gradient methods in hyperbolic space forms.

The aim of the present paper is to provide an intrinsic investigation of projective changes in Finlser geometry, following the pullback formalism. Various known local results are generalized and other new intrinsic results are obtained. Nontrivial characterizations of projective changes are given. The fundamental proje…

The paper studies how points and lines can move while preserving incidences.

The study classifies semiaffine stable planes into affine, projective, or punctured projective planes.

The Willmore energy for Frenet curves in quaternionic projective space is the generalization of the Willmore functional for immersions into the 4-sphere. Critical points of the Willmore energy are called Willmore curves in quaternionic projective space. Using a Baecklund transformation on Willmore curves, we generalize…

Study of hyperbolic directions in convex projective geometry.

In this paper we define strongly projectively flatness of holomorphic maps into the complex Grassmannian manifold, which is a kind of generalization of holomorphic maps into the complex projective space and prove a rigidity of equivariant strongly projectively flat maps of compact simply connected homogeneous Kähler ma…

The study confirms most Cantor sets are in general position for all projections.

The paper is devoted to the investigation of four-dimensional Kahler manifolds admitting non-affine H-projective mappings. We find all such manifolds which are non-Einstein. In the paper also Kahler manifolds admitting infinitesimal H-projective transformations are determined. It is proved that the class of Kahler mani…

We study the six-dimensional pseudo-Riemannian spaces with two time-like coordinates that admit non-homothetic infinitesimal projective transformations. The metrics are manifestly obtained and the projective group properties are determined. We also find a generic defining of projective motion in the 6-dimensional rigid…

Paper studies binary random projections with controllable sparsity patterns for computational and accuracy advantages.

Characterizes projective submanifolds in high dimensions.

The article constructs strong Carrollian geometries at infinity for Ricci flat Einstein manifolds.

Study limits of convex domains in projective plane, proving specific results.

A projective geometry is an equivalence class of torsion free connections sharing the same unparametrised geodesics; this is a basic structure for understanding physical systems. Metric projective geometry is concerned with the interaction of projective and pseudo-Riemannian geometry. We show that the BGG machinery of …

The paper proposes a framework for structured prediction using projection oracles.

The paper identifies all link projections with isolate-region number one.

Free Random Projection enhances reinforcement learning by naturally incorporating hierarchical structure.

We study a notion of convex cocompactness for discrete subgroups of the projective general linear group acting (not necessarily irreducibly) on real projective space, and give various characterizations. A convex cocompact group in this sense need not be word hyperbolic, but we show that it still has some of the good pr…

We consider complex projective structures on Riemann surfaces and their groups of projective automorphisms. We show that the structures achieving the maximal possible number of projective automorphisms allowed by their genus are precisely the Fuchsian uniformizations of Hurwitz surfaces by hyperbolic metrics. More gene…

Researchers found indecomposable Killing tensor fields on quaternionic projective spaces.

We solve the metrisability problem for generic three-dimensional projective structures.

Projects Markovian processes from Itô semimartingales with jumps.

The ability to generalize is an important feature of any intelligent agent. Not only because it may allow the agent to cope with large amounts of data, but also because in some environments, an agent with no generalization capabilities cannot learn. In this work we outline several criteria for generalization, and prese…

Even Artin groups generalize right-angled Artin groups by allowing the labels in the defining graph to be even. In this paper a complete characterization of quasi-projective even Artin groups is given in terms of their defining graphs. Also, it is shown that quasi-projective even Artin groups are realizable by K(pi,1) …

New discriminant analysis using GDS projection improves face recognition.

Holomorphic projective structures and bundles are studied on surfaces, revealing affine spaces of parameters.

This paper generalizes monodromy maps for projective structures with poles.

We define two new notions of projection of a stochastic differential equation (SDE) onto a submanifold: the Ito-vector and Ito-jet projections. This allows one to systematically develop low dimensional approximations to high dimensional SDEs using differential geometric techniques. The approach generalizes the notion o…