Related papers: Some properties of Kaehler submanifolds with recur…
Motivated by a previous work of Zheng and the second named author, we study pinching constants of compact K\"ahler manifolds with positive holomorphic sectional curvature. In particular we prove a gap theorem following the work of Petersen…
Exploiting the special features of four-dimensional Riemannian geometry, we derive topological and rigidity results for hypersurfaces immersed in space forms of dimension 5. First, we provide a complete description of the Weyl tensor for…
The aim of the present paper is to provide an intrinsic investigation of two special Finsler spaces whose defining properties are related to Berwald connection, namely, Finsler space of scalar curvature and of constant curvature. Some…
This paper presents two results in the realm of conformal Kaehler submanifolds. These are conformal immersions of Kaehler manifolds into the standard flat Euclidean space. The proofs are obtained by making a rather strong use of several…
We study the conditions under which a K\"ahlerian structure $(G,J)$ of general natural lift type on the cotangent bundle $T^*M$ of a Riemannian manifold $(M,g)$ has constant holomorphic sectional curvature. We obtain that a certain…
Whenever the N=(2,2) supersymmetry algebra of non-linear sigma-models in two dimensions does not close off-shell, a holomorphic two-form can be defined. The only known superfields providing candidate auxiliary fields to achieve an off-shell…
In this paper, we report a "new" continuity path which links the constant scalar curvature equation to a second order elliptic equation. This is largely an expository article where we describes various aspects of geometry and analysis…
A contact hypersurface in a Kaehler manifold is a real hypersurface for which the induced almost contact metric structure determines a contact structure. We carry out a systematic study of contact hypersurfaces in Kaehler manifolds. We then…
We obtain a Kaehler Einstein structure on the nonzero cotangent bundle of a Riemannian manifold of positive constant sectional curvature. The obtained Kaehler Einstein structure cannot have constant holomorphic sectional curvature and is…
A local classification of the Hermitian manifolds with flat associated connection is given. Hermitian manifolds admitting locally a conformal metric with flat associated connection are characterized by a curvature identity. Locally…
As first noted in Korevaar, Kusner and Solomon ("KKS"), constant mean curvature implies a homological conservation law for hypersurfaces in ambient spaces with Killing fields.In Theorem 3.5 here, we generalize that law by relaxing the…
In this short note, we prove the existence of constant scalar curvature K\"ahler metrics on compact K\"ahler manifolds with semi-ample canonical bundles.
Motivated by understanding the limiting case of a certain systolic inequality we study compact Riemannian manifolds having all harmonic 1-forms of constant length. We give complete characterizations as far as K\"ahler and hyperbolic…
We observe that the maximal open set of constant curvature k in a Riemannian manifold with curvature bounded below or above by k has a convexity type property, which we call "two-convexity". This statement is used to prove a number of…
It is shown that q-deformed quantum mechanics (systems with q-deformed Heisenberg commutation relations) can be interpreted as an ordinary quantum mechanics on Kaehler manifolds, or as a quantum theory with second (or first)- class…
We prove a sharp lower bound for the Tanaka-Webster holomorphic sectional curvature of strictly pseudoconvex real hypersurfaces that are "semi-isometrically" immersed in a K\"ahler manifold of nonnegative holomorphic sectional curvature…
In this short essay, we will survey on two conjectures in non-K\"ahler geometry: the constant holomorphic sectional curvature conjecture and the Fino-Vezzoni conjecture. We aim at the broad audience and assume no expertise in non-K\"ahler…
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.
In an earlier work, we investigated some consequences of the existence of a K\"ahler metric of negative holomorphic sectional curvature on a projective manifold. In the present work, we extend our results to the case of semi-negative (i.e.,…
We characterize Riemannian manifolds of constant sectional curvature in terms of commutation properties of their Jacobi operators.