On the Kobayashi-Royden pseudonorm for almost complex manifolds

1997/08/25 by Boris Kruglikov, Boris S. Kruglikov, Kruglikov, Boris S.
Mathematics · #32H20 #53C15 #53C56 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #dg-ga #math.DG #msc:32H20 #msc:53C15 #msc:53C56

paper · pdf · doi:10.48550/arxiv.dg-ga/9708012

14 pages, La-TeX

arxiv created 1997/08/25 · openalex publication_date 1997/08/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we define Kobayashi-Royden pseudonorm for almost complex manifolds. Its basic properties known from the complex analysis are preserved in the nonintegrable case as well. We prove that the pseudodistance induced by this pseudonorm coincides with the Kobayashi pseudodistance defined for the almost complex case earlier. We also consider a geometric application for moduli spaces of pseudoholomorphic curves.

Related

• Existence of close pseudoholomorphic disks for almost complex manifolds and an applications to Kobayashi-Royden pseudonorm
• The Kobayashi pseudodistance on almost complex manifolds
• Estimates of the Kobayashi metric on almost complex manifolds
• Counterexamples related to the Kobayashi Pseudodistance
• Kobayashi pseudometric on hyperkahler manifolds