Related papers: Kahler submanifolds and the Umehara algebra

The Umehara algebra is studied with motivation on the problem of the non-existence of common complex submanifolds. In this paper, we prove some new results in Umehara algebra and obtain some applications. In particular, if a complex…

Two Kahler manifolds are called relatives if they admit a common Kahler submanifold with the same induced metrics. In this paper, we show that a Hartogs domain over an irreducible bounded symmetric domain equipped with the Bergman metric is…

Let $M_1$ and $M_2$ be two K\"ahler manifolds. We call $M_1$ and $M_2$ {\em relatives} if they share a non-trivial K\"ahler submanifold $S$, namely, if there exist two holomorphic and isometric immersions (K\"ahler immersions) $h_1: S\to…

We study the problem of non-relativity for a complex Euclidean space and a bounded symmetric domain equipped with their canonical metrics. In particular, we answer a question raised by Di Scala. This paper is dedicated to the memory of…

We show that in a certain subfamily of the Kuranishi family of any half Inoue surface the algebraic dimensions of the fibers jump downwards at special points of the parameter space showing that the upper semi-continuity of algebraic…

We give a complete list of non-isometric bidimensional rotation invariant K\"ahler-Einstein submanifolds of a finite dimensional complex projective space endowed with the Fubini-Study metric. This solves in the aforementioned case a…

We give a complete list, for $n \leq 6$, of non-isometric $\mathbb{T}^n$-invariant Kaehler-Einstein manifolds immersed in a finite dimensional complex projective space endowed with the Fubini-Study metric. This solves, in the aforementioned…

We study Lie algebra $\kappa$-deformed Euclidean space with undeformed rotation algebra $SO_a(n)$ and commuting vectorlike derivatives. Infinitely many realizations in terms of commuting coordinates are constructed and a corresponding star…

Let $M_1$ and $M_2$ be two K\"ahler manifolds. One says that $M_1$ and $M_2$ are "relatives" if they share a non-trivial K\"ahler submanifold $S$, namely, if there exist two holomorphic and isometric immersions (K\"ahler immersions) $h_1: S…

For an orientable surface with an area form, there are two invariants of area-preserving dynamics, the flux homomorphism and the Calabi invariant. Tsuboi found a remarkable connection between the Calabi invariant on the closed disk and a…

The general construction of self-adjoint configuration space representations of the Heisenberg algebra over an arbitrary manifold is considered. All such inequivalent representations are parametrised in terms of the topology classes of flat…

We prove that every (compact) taut submanifold in Euclidean space is real algebraic, i.e., is a connected component of a real irreducible algebraic variety in the same ambient space. This answers affirmatively a question of Nicolaas Kuiper…

We consider the dual space of linear groups over Dynkinian and Euclidean algebras, i.e. finite dimensional algebras derived equivalent to the path algebra of Dynkin or Euclidean quiver. We prove that this space contains an open dense subset…

By Hartman--Nirenberg's theorem, any complete flat hypersurface in Euclidean space must be a cylinder over a plane curve. However, if we admit some singularities, there are many non-trivial examples. Flat fronts are flat hypersurfaces with…

We extend the definition of quasi-finite complexes by considering not necessarily countable complexes. We provide a characterization of quasi-finite complexes in terms of L-invertible maps and dimensional properties of compactifications.…

We introduce a new invariant, the real (logarithmic)-Kodaira dimension, that allows to distinguish smooth real algebraic surfaces up to birational diffeomorphism. As an application, we construct infinite families of smooth rational real…

We study group algebras for compact groups in the category of real and complex weakly complete vector spaces. We also show that the group algebra is a quotient of the weakly complete universal enveloping algebra of the Lie algebra of the…

We investigate a class of Leibniz algebroids which are invariant under diffeomorphisms and symmetries involving collections of closed forms. Under appropriate assumptions we arrive at a classification which in particular gives a…

In this paper we give local and global parametric classifications of a class of Einstein submanifolds of Euclidean space. The highlight is for submanifolds of codimension two since in this case our assumptions are only of intrinsic nature.

We study K\"ahler manifolds that are (weak) relatives, that is, K\"ahler manifolds which share a (locally isometric) submanifold. In particular, we prove that if two K\"ahler manifolds are weak relatives and one of them is projective, then…