We derive some consequences of the Liouville theorem for plurisubharmonic functions L.-F. Tam and author. The first result provides a nonlinear version complex splitting (which splits off factor ℂ isometrically from simply connected Kähler manifold with nonnegative bisectional curvature linear growth holomorphic function) second set results concerns so-called k-hyperbolicity its connection nega...

Some observations about the local and global generality of gradient Kähler Ricci solitons are made, including the existence of a canonically associated holomorphic volume form and vector field, the local generality of solutions with a prescribed holomorphic volume form and vector field, and the existence of Poincaré coordinates in the case that the Ricci curvature is positive and the vector fie...

In this work we consider compact Kähler manifolds with non-positive mixed curvature which is a “convex combination” of Ricci and holomorphic sectional curvature. We show that in case, the canonical line bundle nef. Moreover, if negative at some point, then manifold projective being big If addition negative, ample. As an application, answer question Ni [Comm. Pure Appl. Math. 74 (2021), pp. 1100...

We determine a 2-codimensional para-CR structure on the slit tangent bundle T0M of a Finsler manifold (M,F ) by imposing a condition regarding the almost paracomplex structure P associated to F when restricted to the structural distribution of a framed para-f -structure. This condition is satisfied when (M,F ) is of scalar flag curvature (particularly constant) or if the Riemannian manifold (M,...

It is easily seen that the graphs of harmonic conjugate functions (the real and imaginary parts of a holomorphic function) have the same nonpositive Gaussian curvature. The converse to this statement is not as simple. Given two graphs with the same nonpositive Gaussian curvature, when can we conclude that the functions generating their graphs are harmonic? In this paper, we show that given a gr...

We classify the holomorphic structures of the tangent vertical bundle Θ of the twistor fibration of a quaternionic manifold (M,Q) of dimension 4n ≥ 8. In particular, we show that any self-dual quaternionic connection D of (M,Q) induces an holomorphic structure ∂̄ on Θ. We construct a Penrose transform which identifies solutions of the Penrose operator P on (M,Q) defined by D with the space of ∂̄-...

In this paper, we study certain curvature conditions satisfying by the conharmonic curvature tensor in a Lorentzian para-Sasakian manifold with respect to the quarter-symmetric metric connection. AMS Mathematics Subject Classification (2010): 53B05, 53C25

We prove that every Kähler metric, whose potential is a function of the timelike distance in the flat Kähler-Lorentz space, is of quasi-constant holomorphic sectional curvatures, satisfying certain conditions. This gives a local classification of the Kähler manifolds with the above mentioned metrics. New examples of Sasakian space forms are obtained as real hypersurfaces of a Kähler space form ...

Measure contraction properties are generalizations of the notion of Ricci curvature lower bounds in Riemannian geometry to more general metric measure spaces. In this paper, we give sufficient conditions for a contact sub-Riemannian manifold with a one-parameter family of symmetries to satisfy these properties. Moreover, in the special case where the quotient of the contact subRiemannian manifo...