Minimal K\'ahler submanifolds in product of space forms

Autor: de Carvalho, Alcides, Domingos, Iury
Rok vydání: 2021
Předmět:
Druh dokumentu: Working Paper
Popis: In this article, we study minimal isometric immersions of K\"ahler manifolds into product of two real space forms. We analyse the obstruction conditions to the existence of pluriharmonic isometric immersions of a K\"ahler manifold into those spaces and we prove that the only ones into $\mathbb{S}^{m-1}\times\mathbb{R}$ and $\mathbb{H}^{m-1}\times \mathbb{R}$ are the minimal isometric immersions of Riemannian surfaces. Futhermore, we show that the existence of a minimal isometric immersion of a K\"ahler manifold $M^{2n}$ into $\mathbb{S}^{m-1}\times\mathbb{R}$ and $\mathbb{S}^{m-k}\times \mathbb{H}^k$ imposes strong restrictions on the Ricci and scalar curvatures of $M^{2n}$. In this direction, we characterise some cases as either isometric immersions with parallel second fundamental form or anti-pluriharmonic isometric immersions.
Comment: Suggestions and comments are of course welcome
Databáze: arXiv