We study canonical paracontact connection on a para-Sasakian manifold. We prove that a Ricci-flat para-Sasakian manifold with respect to canonical paracontact connection is an η-Einstein manifold.We also investigate some properties of curvature tensor, conformal curvature tensor,W2curvature tensor, concircular curvature tensor, projective curvature tensor, and pseudo-projective curvature tensor...

In this paper, we derive a partial result related to a question of Yau: “Does a simply-connected complete Kähler manifold M with negative sectional curvature admit a bounded non-constant holomorphic function?” Main Theorem. Let M be a simply-connected complete Kähler manifold M with negative sectional curvature ≤ −1 and S∞(M) be the sphere at infinity of M. Then there is an explicit bounded con...

Grauert showed that it is possible to construct complete Kähler metrics on the complement of complex analytic sets in a domain holomorphy. In this note, we study holomorphic sectional curvatures such principal divisor $$\mathbb {C}^n$$ , $$n \ge 1$$ . addition, also how metric and its curvature behave when corresponding divisors vary continuously.

In this paper, we extend the general maximum principle in [NT3] to the time dependent Lichnerowicz heat equation on symmetric tensors coupled with the Ricci flow on complete Riemannian manifolds. As an application we exhibit complete Riemannian manifolds with bounded nonnegative sectional curvature of dimension greater than three such that the Ricci flow does not preserve the nonnegativity of t...

One of the main purpose of this paper is to compare those well-known canonical and complete metrics on the Teichmüller and the moduli spaces of Riemann surfaces. We use as bridge two new metrics, the Ricci metric and the perturbed Ricci metric. We will prove that these metrics are equivalent to those classical complete metrics. For this purpose we study in detail the asymptotic behaviors and th...

Let p : X → S be a smooth Kähler fibration and E → X a Hermitian holomorphic vector bundle. As motivated by the work of Berdtsson([Bern09]), by using basic Hodge theory, we derive several general curvature formulas for the direct image p∗(KX/S ⊗E) for general Hermitian holomorphic vector bundle E in a very simple way. A straightforward application is that, if the Hermitian vector bundle E is Na...

Suppose that M is a complete Kähler manifold such its holomorphic sectional curvature bounded from below by constant and radial also below. N strongly pseudoconvex complex Finsler above negative constant. In this paper, we establish Schwarz lemma for mappings f into N. As applications, obtain Liouville type rigidity result N, as well theorem bimeromorphic compact manifold.

This paper determined the components of generalized curvature tensor for class Kenmotsu type and established mentioned is {\eta}-Einstein manifold when flat; converse holds true under suitable conditions. It also introduced notion {\Phi}-holomorphic sectional (G{\Phi}SH-) thus found necessary sufficient conditions to be constant G{\Phi}SH-curvature. In addition, {\Phi}-generalized semi-symmetri...