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.
Characterizes projective special complex manifolds using c-projective structures.
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.
Listed Kaehler-Einstein manifolds in complex projective spaces.
Study of affine and projective structures on foliated complex manifolds.
Max diameter Kahler manifolds with positive bisectional curvature are complex projective spaces.
Curved 10-manifolds with torus symmetry are spheres or complex projective spaces.
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…
Optimizes energy of mappings from complex projective spaces.
Proves the Hodge conjecture for complex projective 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…
Research explores flat subspaces in complex projective manifolds using Okounkov bodies.
Research confirms a conjecture about complex manifolds with total Betti number three.
New curvature positivity helps classify spherical spaces and complex projective spaces.
Proves projectivity and ampleness of a Kähler manifold using complex Monge-Ampère equation.
Stability results for complex Monge-Ampère equations in various classes.
We show that for any complete connected Kähler manifold the index of the group of complex affine transformations in the group of c-projective transformations is at most two unless the Kähler manifold is isometric to complex projective space equipped with a positive constant multiple of the Fubini-Study metric. This est…
We introduce the concept of a branched holomorphic Cartan geometry. It generalizes to higher dimension the definition of branched (flat) complex projective structure on a Riemann surface introduced by Mandelbaum. This new framework is much more flexible than that of the usual holomorphic Cartan geometries. We show that…
We develop in detail the theory of c-projective geometry, a natural analogue of projective differential geometry adapted to complex manifolds. We realise it as a type of parabolic geometry and describe the associated Cartan or tractor connection. A Kaehler manifold gives rise to a c-projective structure and this is one…
Study complex quaternionic manifolds and their c-projective structures.
Classifies holomorphic parabolic geometries on complex manifolds.
Classify projective subvarieties in Bogomolov-Guan manifolds using quasi-diagonals.
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…
Lecture notes on curves in complex projective plane from a topological viewpoint.
Extremal Kähler submanifolds of complex projective spaces have natural extensions.
Researchers compute c-projective symmetry algebras for Kähler surfaces.
Extends Tian theorem to Vaisman manifolds for approximations.
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.
The paper finds transformation formulas for quaternionic complex structures.
We develop some theory of double fibration transforms where the cycle space is a smooth manifold and apply it to complex projective space.
Study on Gauduchon manifolds finds metrics for projectively flat bundles.
Zoll manifolds with entire Grauert tubes are proven to be standard complex projective spaces.
The study shows conditions for Kähler manifolds to have rational cohomology of complex projective space.
The main theorem of this paper is a result of estimated transversality with respect to stratifications of jet spaces in the approximately holomorphic category over an almost-complex manifold. The notion of asymptotic ampleness of complex vector bundles over an almost-complex manifold is also discussed, as well as appli…
Bounding geodesic length variation for surface projective structures.
Two Kähler metrics on a complex manifold are called c-projectively equivalent if their -planar curves coincide. These curves are defined by the property that the acceleration is complex proportional to the velocity. We give an explicit local description of all pairs of c-projectively equivalent Kähler metrics of arb…
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…
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.
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 …
Study of quasi-Kähler metrics on complex manifolds linked to c-projective metrizability.
We construct a family of canonical connections and surrounding basic theory for almost complex manifolds that are equipped with an affine connection. This framework provides a uniform approach to treating a range of geometries. In particular we are able to construct an invariant and efficient calculus for conformal alm…
New upper bound for geodesic complexity derived from cut locus decompositions.
An orientation preserving diffeomorphism over a surface embedded in a 4-manifold is called extendable, if this diffeomorphism is a restriction of an orientation preserving diffeomorphism on this 4-manifold. In this paper, we investigate conditions for extendability of diffeomorphisms over surfaces in the complex projec…
We investigate compact Kahler manifolds, which are acted on by a semisimple compact Lie group G of isometries with one hypersurface orbit. In case of ordinary action and projectable complex structure, we set up a one to one correspondence between such manifolds and abstract models. The Ricci tensor is then computed and…
We study the global property of local holomorphic isometric mappings from a class of Kahler manifolds into a product of projective algebraic manifolds with induced Fubini-Study metrics, where isometric factors are allowed to be negative.
The paper proves a conjecture about the positivity of the Euler characteristic for complex projective manifolds.
Almost complex structures found on many homotopy complex projective spaces.
The paper proves properties of complex manifolds with nonnegative holomorphic sectional curvature.
Compact Kähler manifold minus a divisor is projective space.