A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Sharp bounds found for energy in projective space mappings.
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…
In this paper we study the set of projective maps between compact proper convex real projective manifolds. We show that this set contains only finitely many distinct homotopy classes and each homotopy class has the structure of a real projective manifold. When the target manifold is strictly convex, our results imply t…
Optimizes energy of mappings from complex projective spaces.
New framework uses elliptic operators to study projective maps.
Researchers found uncountable harmonic self-maps in complex projective spaces.
Paper defines conditions for projective links in projective 3-space.
Study on unique generalized Gauss maps of minimal surfaces sharing hypersurfaces in projective varieties.
Study energy-minimizing maps in projective spaces, proving sharp bounds.
We consider equitorsion second type almost geodesic mappings of a non-symmetric affine connection space in this article. Using different computational methods, we obtained some invariants of these mappings. Last generalized Thomas projective parameter and Weyl projective tensor as invariants of a second type almost geo…
For any two disjoint oriented circles embedded into the 3-dimensional real projective space, we construct a 3-dimensional configuration space and its map to the projective space such that the linking number of the circles is the half of the degree of the map. Similar interpretations are given for the linking number of …
Study identifies subvarieties of projective varieties mapping to models.
This article shows that every non-isotropic harmonic 2-torus in complex projective space factors through a generalised Jacobi variety related to the spectral curve. Each map is composed of a homomorphism into the variety and a rational map off it. The same ideas allow one to construct (pluri)-harmonic maps of finite ty…
A projection maps geodesic currents to Teichmüller space.
Develop a framework for barycentric projections of optimal transport plans on Riemannian manifolds.
Study proves rigidity of harmonic maps from 2-torus to complex projective space.
We show that the moduli space of genus zero stable maps is a real projective variety if the target space is a smooth convex real projective variety. We show that evaluation maps, forgetful maps are real morphisms. We analyze the real part of the moduli space.
New quantity helps map homotopy classes in complex spaces.
Maps from 2-planes to projective spaces using quaternions and octonions.
We describe some general constructions on a real smooth projective 4-quadric which provide analogues of the Willmore functional and conformal Gauss map in both Lie sphere and projective differential geometry. Extrema of these functionals are characterized by harmonicity of this Gauss map.
This paper generalizes monodromy maps for projective structures with poles.
Paper proves unique tangent maps for complex maps into algebraic varieties.
New real algebraic maps with prescribed images and compositions are constructed locally like moment maps.
Study of Demoulin surfaces using Gauss maps and conformal coordinates.
For a surface in the 3-dimensional real projective space, we define a Gauss map, which is a quadric in and called the first-order Gauss map. It will be shown that the surface is a Demoulin surface if and only if the first-order Gauss map is conformal, and the surface is a projective minimal coincidence …
Random projections help in representing sparse graphs efficiently.
We studied rules of transformations of Christoffel symbols under third type almost geodesic mappings in this paper. From this research, we obtained some new invariants of these mappings. These invariants are analogies of Thomas projective parameter and Weyl projective tensor.
Two projective structures on Riemann surfaces are described and shown not to be identical.
We determine all complete projective special real surfaces. By the supergravity r-map, they give rise to complete projective special Kähler manifolds of dimension 6, which are distinguished by the image of their scalar curvature function. By the supergravity c-map, the latter manifolds define in turn complete quaternio…
We apply the recent results of Galkin et al. [GKMS15] to study some geometrical features of Keum's fake projective planes. Among other things, we show that the bicanonical map of Keum's fake projective planes is always an embedding. Moreover, we construct a nonstandard exceptional collection on the unique fake projecti…
Euler and Delisle developed a map method for the Russian Empire, which is now outperformed by the Lambert conformal conical projection.
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…
This study is motivated by the researches in the field of invariants of geodesic and conformal mappings presented in (T. Y. Thomas, [22]) and (H. Weyl, [25]). The Thomas projective parameter and the Weyl projective tensor are generalized in this article. Generators for vector spaces of invariants of geometric mappings …
This paper constructs real algebraic maps that are topologically special generic maps.
-deformability of maps into projective space is characterised by the existence of certain Lie algebra valued 1-forms. This characterisation gives a unified way to obtain well known results regarding deformability in different geometries.
Unique maximal curve systems found for up to 5 punctures.
We consider the quasiconformal dilatation of projective transformations of the real projective plane. For non-affine transformations, the contour lines of dilatation form a hyperbolic pencil of circles, and these are the only circles that are mapped to circles. We apply this result to analyze the dilatation of the circ…
We formulate a correspondence between affine and projective special Kähler manifolds of the same dimension. As an application, we show that, under this correspondence, the affine special Kähler manifolds in the image of the rigid r-map are mapped to one-parameter deformations of projective special Kähler manifolds in t…
Study maps in semidirect products of groups, proving Lipschitz properties without intrinsic dilations.
The author studies regions foliated by 1D families of functions and their applications.
We classify all complete projective special real manifolds with reducible cubic potential, obtaining four series. For two of the series the manifolds are homogeneous, for the two others the respective automorphism group acts with co-homogeneity one. Complete projective special real manifolds give rise to complete quate…
The paper optimizes Dirac eigenvalues on surfaces and connects them to harmonic maps into complex projective spaces.
Abstract: Mapping class groups act on cohomology of surfaces via Hochschild cohomology.
The paper calculates the mapping class group of specific complex projective plane bundles.
The paper improves defect relations for Gauss maps of minimal surfaces intersecting hypersurfaces in projective space.
Let G be a complex reductive group and K a maximal compact subgroup. If X is a smooth projective G-variety, with a fixed (not necessarily integral) K-invariant Kaehler form, then the K-action is Hamiltonian. Let M be the zero fiber of the corresponding moment map. It is well known that the quotient M/K is a complex spa…
General invariants of a geometric mapping of a symmetric affine connection space are obtained in this paper. These invariants are generalizations of the previous obtained basic invariants (see [16]). Moreover, these invariants are related with the Thomas projective parameter and the Weyl projective tensor.
Paper proposes PPMM for fast estimation of large-scale OTM.