arXiv research

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…

Classifies actions on complex space forms with Lagrangian orbits.

New condition prevents hyperbolic spaces from matching curve complexes.

Classifies minimal submanifolds in complex hyperbolic spaces.

New curvature positivity helps classify spherical spaces and complex projective spaces.

We obtain a new differentiable sphere theorem for compact Lagrangian submanifolds in complex Euclidean space and complex projective space.

Proves conjecture on graph configuration spaces' complexity.

Paper constructs Hopf real hypersurfaces in complex hyperbolic space.

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 moduli space of Higgs bundles is stratified into complex symplectic submanifolds.

The study of real hypersurfaces in pseudo-Riemannian complex space forms and para-complex space forms, which are the pseudo-Riemannian generalizations of the complex space forms, is addressed. It is proved that there are no umbilic hypersurfaces, nor real hypersurfaces with parallel shape operator in such spaces. Denot…

Study examines Kähler immersions of ALE Kähler metrics into complex space forms.

Unique inhomogeneous ruled hypersurface found in complex hyperbolic space.

Classifies CR submanifolds in complex hyperbolic spaces.

Extremal Kähler submanifolds of complex projective spaces have natural extensions.

Study geometry of tetrahedra in complex hyperbolic space and Hilbert spaces.

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

We introduce integrable complex structures on twistor spaces fibered over complex manifolds. We then show, in particular, that the twistor spaces associated with generalized Kahler, SKT and strong HKT manifolds all naturally admit complex structures. Moreover, in the strong HKT case we construct a metric and three comp…

Link condition for simplicial complexes to be CUB spaces.

It is proved, that if M is a connected, complete submanifold of a complex space form N and each geodesic of M lies in an 1-dimensional totally geodesic complex submanifold of N, then M is totally geodesic in N and is a real space form or a complex space form.

Paper addresses hidden faces in configuration space integrals for embeddings.

The study constructs minimal submanifolds in complex and quaternionic projective spaces.

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…

The space ${\mathcal A}$ of almost complex structures on a closed manifold $M$ is studied. A natural parametrization of the space ${\mathcal A}$ is defined. It is shown, that ${\mathcal A}$ is a infinite dimensional complex weak Pseudo-Riemannian manifold. A curvature of the space ${\mathcal A}$ is found. The space ${\…

We combine aspects of the notions of finite decomposition complexity and asymptotic property C into a notion that we call finite APC-decomposition complexity. Any space with finite decomposition complexity has finite APC-decomposition complexity and any space with asymptotic property C has finite APC-decomposition comp…

We use the Grauert--Grothendieck complex on differentiable spaces to study basic relative forms on the inertia space of a compact Lie group action on a manifold. We prove that the sheaf complex of basic relative forms on the inertia space is a fine resolution of Bryliski's sheaf of functions on the inertia space.

New non-trivial Kaehler-Ricci solitons found in infinite dimensional complex space forms.

We define the surface complex for $3$-manifolds and embark on a case study in the arena of Seifert fibered spaces. The base orbifold of a Seifert fibered space captures some of the topology of the Seifert fibered space, so, not surprisingly, the surface complex of a Seifert fibered space always contains a subcomplex is…

New probabilistic invariants bound classical topological complexity and category.

Survey on complex submanifolds in Euclidean spaces.

We complete our recent classification of compact inner symmetric spaces with weakly complex tangent bundle by filling up a case which was left open, and extend this classification to the larger category of compact homogeneous spaces with positive Euler characteristic. We show that a simply connected compact equal rank …

We introduce curvature-adapted foliations of complex hyperbolic space and study some of their properties. Generalized pseudo-Einstein hypersurfaces of complex hyperbolic space are classified. Analogous results for curvature-adapted hypersurfaces of quaternionic hyperbolic space are also obtained.

In this paper, we study the complex Landsberg spaces and some of their important subclasses. We introduce and characterize the class of generalized Berwald and complex Landsberg spaces. The intersection of these spaces gives the so called $G-$ Landsberg class.

Study shows a copy of 7D real projective space in the space of almost complex structures on 6-sphere.

New RL method reduces sample complexity for large policy spaces.

Study real hypersurfaces in complex space forms for an inequality involving a contact invariant.

An isometric immersion $f:M^n\to \tilde M^n$ from a Riemannian $n$-manifold $M^n$ into a Kähler $n$-manifold $\tilde M^n$ is called {\it Lagrangian} if the complex structure $J$ of the ambient manifold $\tilde M^n$ interchanges each tangent space of $M^n$ with the corresponding normal space. In this paper, we completel…

Study on PMC surfaces in complex space forms, linking biconservative and totally real properties.

For a genus two Heegaard splitting of a lens space, the primitive disk complex is defined to be the full subcomplex of the disk complex for one of the handlebodies of the splitting spanned by all vertices of primitive disks. In this work, we describe the complete combinatorial structure of the primitive disk complex fo…

Study almost complex structures on six-manifolds using twistor spaces.

In this paper, the concept of balanced manifolds is generalized to reduced complex spaces: the class B and balanced spaces. Compared with the case of Kahlerian, the class B is similar to the Fujiki class C and the balanced space is similar to the Kahler space. Some properties about these complex spaces are obtained, an…

This paper classifies Ricci solitons in complex hyperbolic spaces.

Researchers create a new metric on complex projective space bundles.

Almost complex structures found on many homotopy complex projective spaces.

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.

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…

Complex of cuts reveals full automorphism group for certain Stone spaces.

We classify real hypersurfaces in complex space forms with constant principal curvatures and whose Hopf vector field has two nontrivial projections onto the principal curvature spaces. In complex projective spaces such real hypersurfaces do not exist. In complex hyperbolic spaces these are holomorphically congruent to …