Related papers: The homogeneous slice theorem for the complete com…
We show that a totally geodesic submanifold of a symmetric space satisfying certain conditions admits an extension to a minimal submanifold of dimension one higher, and we apply this result to construct new examples of complete embedded…
In a previous paper Affine symmetries of the equivariant quantum cohomology of rational homogeneous spaces, a general formula was given for the multiplication by some special Schubert classes in the quantum cohomology of any homogeneous…
We classify contact manifolds $(M,\mathcal D)$ which are homogeneous under a connected semisimple Lie group $G$, and symmetric in the sense that there exists a contactomorphism of $(M,\mathcal D)$ normalizing $G$, fixing a point $o$ in $M$…
We define the notion of complex stratification by quasifolds and show that such spaces occur as complex quotients by certain nonclosed subgroups of tori associated to convex polytopes. The spaces thus obtained provide a natural…
Let K be a compact Lie group. We compute the abelianization of the Lie algebra of equivariant vector fields on a smooth K-manifold X. We also compute the abelianization of the Lie algebra of strata preserving smooth vector fields on the…
We prove a complex polynomial plank covering theorem for not necessarily homogeneous polynomials. As the consequence of this result, we extend the complex plank theorem of Ball to the case of planks that are not necessarily centrally…
Given a compact smooth manifold $M$ with non-empty boundary and a Morse function, a pseudo-gradient Morse-Smale vector field adapted to the boundary allows one to build a Morse complex whose homology is isomorphic to the (absolute or…
We show that a compact representation of a semisimple Lie group has an orthogonal decomposition into finite length representations. This generalises and simplifies a number of more special spectral theorems in the literature. We apply it to…
The notion of a holomorphically symplectic manifold can be generalized to the singular one. This paper studies the birational contraction maps between symplectic varieties, and then describes the deformation of a symplectic variety which…
In this paper we study transversely holomorphic foliations of complex codimension one with some hypothesis on the transverse structure.
We investigate the cohomology of a certain elliptic complex defined on a compact quaternionic-K\"{a}hler manifold with negative scalar curvature. We show that this particular complex is exact, with the possible exception of one term.
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…
Homotopy connectedness theorems for complex submanifolds of homogeneous spaces (sometimes referred to as theorems of Barth-Lefshetz type) have been established by a number of authors. Morse Theory on the space of paths lead to an elegant…
In this paper an extended CPR decomposition theorem for Finsler symmetric spaces of semi-negative curvature in the context of reductive structures is proven. This decomposition theorem is applied to give a geometric description of the…
We determine the symmetrized topological complexity of the circle, using primarily just general topology.
In this note, we survey our recent work concerning cohomologies of harmonic bundles on quasi-compact Kaehler manifolds.
A foliation on a Riemannian manifold is hyperpolar if it admits a flat section, that is, a connected closed flat submanifold that intersects each leaf of the foliation orthogonally. In this article we classify the hyperpolar homogeneous…
We prove a coherence theorem for invertible objects in a symmetric monoidal category. This is used to deduce associativity, skew-commutativity, and related results for multi-graded morphism rings, generalizing the well-known versions for…
We complete the classification of isometric cohomogeneity-one actions on all symmetric spaces of noncompact type up to orbit equivalence.
We introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.