Related papers: Aspects of the Levi form
The purpose of the present paper is to study the differential geometric properties of a quaternion CR-submanifold in a locally conformal quaternion Kaehler manifold.
We find the precise growth of some invariant metrics near a point on the boundary of a domain where the Levi form has at least one negative eigenvalue. We also introduce a new invariant pseudometric which is convenient in this context, and…
This is a survey of the geometry of complex cubic fourfolds with a view toward rationality questions. Topics include classical constructions of rational examples, Hodge structures and special cubic fourfolds, associated K3 surfaces and…
We prove the existence and uniqueness of Levi-Civita connections for strongly sigma-compatible pseudo-Riemannian metrics on tame differential calculi. Such pseudo-Riemannian metrics properly contain the classes of bilinear metrics as well…
The topics of Convexity and Concavity and Envelopes are central in Complex Analysis and extensively investigated. The aim of this paper is to find a possible counterpart in Algebraic Geometry. The article presents preliminary results on…
The present paper deals with the study of totally real submanifolds and $\textit{C}$-totally real submanifolds of $(LCS)_n$-manifolds with respect to Levi-Civita connection as well as quarter symmetric metric connection. It is proved that…
We study deformations of complex projective varieties that are homotopically or homologically trivial. We formulate several conjectures and give some examples and partial answers.
We define a complex connection on a real hypersurface of $\C^{n+1}$ which is naturally inherited from the ambient space. Using a system of Codazzi-type equations, we classify connected real hypersurfaces in $\C^{n+1}$, $n\ge 2$, which are…
We study curvature restrictions of Levi-flat real hypersurfaces in complex projective planes, whose existence is in question. We focus on its totally real Ricci curvature, the Ricci curvature of the real hypersurface in the direction of the…
The purpose of this article is to classify the real hypersurfaces in complex space forms of dimension 2 that are both Levi-flat and minimal. The main results are as follows: When the curvature of the complex space form is nonzero, there is…
Starting from a cubic form, we give a general construction of a quasi-complete homogeneous manifold endowed with a natural contact structure. We show that it can be compactified into a projective contact manifold if and only if the cubic…
We show that every formal embedding sending a real-analytic strongly pseudoconvex hypersurface in $M\subset \C^N$ into another such hypersurface in $M'\subset \C^{N+1}$ is convergent. More generally, if $M$ and $M'$ are merely…
We investigate a few aspects of the notion of Levi core, introduced by the authors in a previous work: a basic finiteness question, the connections with Kohn's algorithm and with Catlin's property (P).
Object of investigation are almost hypercomplex manifolds with Hermitian-Norden metrics of the lowest dimension. The considered manifolds are constructed on 4-dimensional Lie groups. It is established a relation between the classes of a…
We search for Riemannian metrics whose Levi-Civita connection belongs to a given projective class. Following Sinjukov and Mikes, we show that such metrics correspond precisely to suitably positive solutions of a certain projectively…
Almost contact manifolds with B-metric are considered. Of special interest are the so-called vertical classes of the almost contact B-metric manifolds. Curvature properties of these manifolds are studied. An example of 5-dimensional…
Generalized differential forms are used in discussions of metric geometries and Einstein's vacuum field equations. Cartan's structure equations are generalized and applied. In particular flat generalized connections are associated with any…
This research article introduces the concept of lightlike submanifolds of an indefinite Kenmotsu statistical manifold. Various results on geometry of contact CR and SCR-lightlike submanifolds have been developed. Some characterization…
Some aspects of the multidimensional soliton geometry are considered.
This paper, sixth in a series of eight, uses the geometric calculus on manifolds developed in previous papers of the series to introduce through the concept of a metric extensor field g a metric structure for a smooth manifold M. The…