Related papers: CR-submanifolds. A class of examples
In this paper I have studied about CR(Cauchy-Riemann)-submanifolds of Lorentzian Concircular Structure manifold ((LCS)n-manifold), Lorentzian Para-Sasakian(LP)-cosymplectic manifold, S-manifold and Generalized Kenmotsu (GKM) manifold. I…
A method is proposed to obtain examples of smooth CR-manifolds whose local stability group is neither a Lie group nor infinite-dimensional.
In this article we show how holomorphic Riemannian geometry can be used to relate certain submanifolds in one pseudo-Riemannian space to submanifolds with corresponding geometric properties in other spaces. In order to do so, we shall first…
We consider complex manifolds that admit actions by holomorphic transformations of classical simple real Lie groups and classify all such manifolds in a natural situation. Under our assumptions, which require the group at hand to be…
CR singularities of real 4-submanifolds in complex 3-space are classified by using local holomorphic coordinate changes to transform the quadratic coefficients of the real analytic defining equation into a normal form. The quadratic…
We generalize the notion of calibrated submanifolds to smooth maps and show that the several examples of smooth maps appearing in the differential geometry become the examples of our situation. Moreover, we apply these notion to give the…
In two previous papers, we constructed two modified Hamiltonian formalisms to make maps among manifolds explicit. In this paper, the two modified formalisms were adapted to manifolds with local coordinates given by scalar fields, as in a…
We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture) that can be put into correspondence with the usual…
We study submanifolds whose principal curvatures, counted with multiplicities, do not depend on the normal direction. Such submanifolds, which we briefly call CPC submanifolds, are always austere, hence minimal, and have constant principal…
We construct group-invariant CR maps from the unit sphere in $\mathbb{C}^3$ and provide sharp bounds for the gap termination in this setting.
In this paper we introduce the concept of inflexible $CR$ submanifolds. These are $CR$ submanifolds of some complex Euclidean space such that any compactly supported $CR$ deformation is again globally $CR$ embeddable into some complex…
We characterize certain CR structures of arbitrary codimension (different from 3, 4 and 5) on Riemannian Spin$^c$ manifolds by the existence of a Spin$^c$ structure carrying a strictly partially pure spinor field. Furthermore, we study the…
Every action on a Poisson manifold by Poisson diffeomorphisms lifts to a Hamiltonian action on its symplectic groupoid which has a canonically defined momentum map. We study various properties of this momentum map as well as its use in…
We classify all momentum polytopes of rank one for multiplicity free quasi-Hamiltonian $K$-manifolds for simple and simply connected Lie groups $K$ by using the methods developed in a recent paper by F. Knop. This leads to lots of new…
In this paper we complete the classification of spin manifolds admitting parallel spinors, in terms of the Riemannian holonomy groups. More precisely, we show that on a given n-dimensional Riemannian manifold, spin structures with parallel…
This is an example on the cohomology of threefolds.
We describe how the loop group maps corresponding to special submanifolds associated to integrable systems may be thought of as certain Grassmann submanifolds of infinite dimensional homogeneous spaces. In general, the associated families…
We give examples of cohomological automorphic forms for unitary groups which are $p$-adically rigid.
We discuss the relationship between some groups of tangential CR cohomology of some compact homogeneous CR manifolds and the corresponding Dolbeault cohomology groups of their canonical complex embeddings.
E. Cartan's method of moving frames is applied to 3-dimensional manifolds $M$ which are CR-embedded in 5-dimensional real hyperquadrics $Q$ in order to classify $M$ up to CR symmetries of $Q$ given by the action of one of the Lie groups…