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.
New curvature positivity helps classify spherical spaces and complex projective spaces.
Projective rigidity of circle packings on complex surfaces proved.
Killing tensors on complex projective space are identified and generated by Killing fields.
The study constructs minimal submanifolds in complex and quaternionic projective spaces.
Extremal Kähler submanifolds of complex projective spaces have natural extensions.
Classifies foliations of complex and quaternionic projective spaces.
In this paper the projective curvature invariants of a complex Finsler space are obtained. By means of these invariants the notion of complex Douglas space is then defined. A special approach is devoted to obtain the equivalence conditions that a complex Finsler space should be Douglas. It is shown that any weakly Kähl…
The study classifies stable submanifolds in product spaces of projective spaces.
We obtain a new differentiable sphere theorem for compact Lagrangian submanifolds in complex Euclidean space and complex projective space.
Optimizes energy of mappings from complex projective spaces.
Researchers create a new metric on complex projective space bundles.
Solves classical problem with Kähler-Einstein metrics in complex projective spaces.
Listed Kaehler-Einstein manifolds in complex projective spaces.
We give a complete construction of the Bernstein-Gelfand-Gelfand complex on real or complex projective space using minimal ingredients.
In this paper, we first provide an updated survey of the geometry of complex Cartan spaces. New characterizations for some particular classes of complex Cartan spaces are pointed out, e.g. Landsberg-Cartan, strongly Berwald-Cartan and others. We introduce the Cartan-Randers spaces which offer examples of Berwald-Cartan…
Various complexes of differential operators are constructed on complex projective space via the Penrose transform, which also computes their cohomology.
Estimates Schwarzian derivative on long complex projective tubes.
Determines higher smooth surgery structure sets of complex projective spaces.
Max diameter Kahler manifolds with positive bisectional curvature are complex projective spaces.
Curved 10-manifolds with torus symmetry are spheres or complex projective spaces.
For a complex projective space the inertia group, the homotopy inertia group and the concordance inertia group are isomorphic. In complex dimension 4n+1, these groups are related to computations in stable cohomotopy. Using stable homotopy theory, we make explicit computations to show that the inertia group is non-trivi…
Compact RCD spaces derived from singular Kahler metrics on 3D projective varieties.
New characterizations of ruled real hypersurfaces in complex projective space found.
Close to complex projective spaces, Ricci shrinkers are rigid.
We study the moduli space of CR-projective complex foliated tori. We describe it in terms of isotropic subspaces of Grassmannian and we show that it is a normal complex analytic space.
Researchers found indecomposable Killing tensor fields on quaternionic projective spaces.
We develop some theory of double fibration transforms where the cycle space is a smooth manifold and apply it to complex projective space.
Every lens space has a locally flat embedding in a connected sum of 8 copies of the complex projective plane and a smooth embedding in n copies of the complex projective plane for some positive integer n. We show that there is no n such that every lens space smoothly embeds in n copies of the complex projective plane.
Almost complex structures found on many homotopy complex projective spaces.
We describe the fundamental groups of ordered and unordered k point sets in complex projective space of dimension n generating a projective subspace of dimension i. We apply these to study connectivity of more complicated configurations of points.
Motivated by Gray's work on tube formulae for complex submanifolds of complex projective space equipped with the Fubini-Study metric, Riemannian foliations of projective space are studied. We prove that there are no complex Riemannian foliations of any open subset of of codimension one. As a consequence …
It is shown that moduli spaces of complete families of compact complex hypersurfaces in complex manifolds often come equipped canonically with projective structures satisfying some natural integrability conditions.
Researchers found uncountable harmonic self-maps in complex projective spaces.
Irreducible isoparametric foliations of arbitrary codimension q on complex projective spaces CP^n are classified, except if n=15 and q=1. Remarkably, there are noncongruent examples that pull back under the Hopf map to congruent foliations on the sphere. Moreover, there exist many inhomogeneous isoparametric foliations…
We prove an inequality between the sum of the Betti numbers of a complex projective manifold and its total curvature, and we characterize the complex projective manifolds whose total curvature is minimal. These results extend the classical theorems of Chern and Lashof to complex projective space.
Characterizes projective special complex manifolds using c-projective structures.
Study on moduli spaces of branched projective structures on surfaces.
Study proves rigidity of harmonic maps from 2-torus to complex projective space.
A theorem of Lawson and Simons states that the only stable minimal submanifolds in complex projective spaces are complex submanifolds. We generalize their result to the cases of quaternionic and octonionic projective spaces. Our approach gives a unified viewpoint towards conformal and projective geometries.
Study energy-minimizing maps in projective spaces, proving sharp bounds.
We study the limits of sequences of spheres and complex projective spaces with unbounded dimensions. A sequence of spheres (resp. complex projective spaces) either is a Levy family, infinitely dissipates, or converges to (resp. the Hopf quotient of) a virtual infinite-dimensional Gaussian space, depending on the size o…
Analyzes the moduli space of Higgs bundles to prove its quasi-projectivity.
We extend T. Y. Thomas's approach to the projective structures, over the complex analytic category, by involving the -connections. This way, a better control of the projective flatness is obtained and, consequently, we have, for example, the following application: if the twistor space of a quaternionic manifold …
We construct examples of cohomogeneity one special Lagrangian submanifolds in the cotangent bundle over the complex projective space, whose Calabi-Yau structure was given by Stenzel. For each example, we describe the condition of special Lagrangian as an ordinary differential equation. Our method is based on a moment m…
Study shows non-existence of almost complex structures on certain sphere bundles over complex projective spaces.
The object of this article is to compute the holonomy group of the normal connection of complex parallel submanifolds of the complex projective space. We also give a new proof of the classification of complex parallel submanifolds by using a normal holonomy approach. Indeed, we explain how these submanifolds can be reg…
We prove a Berger type theorem for the normal holonomy group (i.e., the holonomy group of the normal connection) of a full complete complex submanifold of the complex projective space. Namely, if the normal holonomy does not act transitively, then the submanifold is the complex orbit, in the complex projective space, o…
Study on Einstein metrics on complex projective spaces with specific group actions.