English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we introduce a new energy density function $\mathscr Y$ on theprojective bundle $\mathbb{P}(T_M)\>M$ for a smooth map $f:(M,h)\>(N,g)$between Riemannian manifolds $$\mathscr Y=g_{ij}f^i_\alpha f^j_\beta\frac{W^\alpha W^\beta}{\sum h_{\gamma\delta} W^\gamma W^\delta}.$$ We get newHessian estimates to this energy density and obtain various new Liouville typetheorems for holomorphic maps, harmonic maps and pluri-harmonic maps. Forinstance, we show that there is no non-constant holomorphic map from a compact\emph{Hermitian manifold} with positive (resp. non-negative) holomorphicsectional curvature to a \emph{Hermitian manifold} with non-positive (resp.negative) holomorphic sectional curvature.

RC-positivity and the generalized energy density I: Rigidity