水平位似淹没与非负曲率

Kähler-Ricci flow and conformal submersion

We study singularity formation of Kähler-Ricci flow on a Kähler manifold that admits a horizontally homothetic conformal submersion into another Kähler manifold. We will derive necessary and sufficient conditions for the preservation of horizontally homothetic conformal submersion along the flow and establish the formation of type I singularity together with a standard splitting of the Cheeger-Gromov limit. This generalizes the setup of Calabi symmetry that was discussed in \cite{1} and \cite{2}, thus gives new proofs for the results listed there.

从Kenmotsu流形到黎曼流形的反不变黎曼浸入

Anti-invariant Riemannian Submersions from Kenmotsu Manifolds onto Riemannian manifolds

研究了从Kenmotsu流形到黎曼流形的反不变黎曼浸入。证明了这方面的几个基本结果。研究了分布的可积性和叶理的几何性质。证明了不存在从Kenmotsu流形到黎曼流形的（反不变）黎曼浸没，使得特征向量场为垂直向量场.给出了一种从翘曲积流形到黎曼流形的水平共形浸入例子的方法。此外，给出了特征向量场为水平向量场时的反不变黎曼浸没和特征向量场为垂直向量场时的反不变水平共形浸没的例子.

Almost h-conformal slant submersions from almost quaternionic Hermitian manifolds

We introduce the notions of h-conformal slant submersions and almost h-conformal slant submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds as a generalization of Riemannian submersions, horizontally conformal submersions, slant submersions, h-slant submersions, almost h-slant submersion and conformal slant submersions. We investigate several properties of these including the integrability of distributions, the geometry of foliations and the conditions for such maps to be totally geodesic. Further we give some examples of such maps.

Almost h-conformal semi-invariant submersions from almost quaternionic Hermitian manifolds

As a generalization of Riemannian submersions, horizontally conformal submersions, semi-invariant submersions, h-semi-invariant submersions, almost h-semi-invariant submersions, conformal semi-invariant submersions, we introduce h-conformal semi-invariant submersions and almost h-conformal semi-invariant submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds. We study their properties: the geometry of foliations, the conditions for total manifolds to be locally product manifolds, the conditions for such maps to be totally geodesic, etc. Finally, we give some example…

Generalized harmonic morphisms and horizontally weakly conformal biharmonic maps

Harmonic morphisms are maps between Riemannian manifolds that pull back harmonic functions to harmonic functions. These maps are characterized as horizontally weakly conformal harmonic maps and they have many interesting links and applications to several areas in mathematics (see the book by Baird and Wood for details). In this paper, we study generalized harmonic morphisms which are defined to be maps between Riemannian manifolds that pull back harmonic functions to biharmonic functions. We obtain some characterizations of generalized harmonic morphisms into a Euclidean space and give two met…

Conformal slant submersions in contact geometry

Akyol M.A. [Conformal anti-invariant submersions from cosymplectic manifolds, Hacettepe Journal of Mathematics and Statistic, 46(2), (2017), 177-192.] defined and studied conformal anti-invariant submersions from cosymplectic manifolds. The aim of the present paper is to define and study the notion of conformal slant submersions (it means the Reeb vector field $ξ$ is a vertical vector field) from almost contact metric manifolds onto Riemannian manifolds as a generalization of Riemannian submersions, horizontally conformal submersions, slant submersions and conformal anti-invariant submersions.…