Remark on quasi-negative $k$-Ricci curvature

In this note, we show that if $X$ is a compact Kähler manifold with $k$-quasi-negative Ricci curvature, then $K_X$ is ample. This completes a previous result of Chu-Lee-Tam. The key ingredient is an observation that any rational curve $C$ on $X$ satisfy $K_X\cdot C>0$ based on the Gauss-Codazzi equation.

Publication Details

Journal
ArXiv.org
Published
2025-08-24
Primary Topic
Geochemistry and Geologic Mapping
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

Remark on quasi-negative $k$-Ricci curvature

ArXiv.org
Geochemistry and Geologic Mapping
article

Remark on quasi-negative $k$-Ricci curvature

article en

Abstract

In this note, we show that if $X$ is a compact Kähler manifold with $k$-quasi-negative Ricci curvature, then $K_X$ is ample. This completes a previous result of Chu-Lee-Tam. The key ingredient is an observation that any rational curve $C$ on $X$ satisfy $K_X\cdot C>0$ based on the Gauss-Codazzi equation.

ArXiv.org
Openalex Percentile: Top 64%
Geochemistry and Geologic Mapping
Open Access PDFOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Remark on quasi-negative $k$-Ricci curvature · ArXiv.org (2025) | TGRS Research Map | TGRS