Invariant operators on manifolds with almost Hermitian symmetric structures, I. Invariant differentiation

1995/03/09 by Andreas Cap, Andreas Čap, Jan Slovak +6 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #dg-ga #math.DG

paper · pdf · doi:10.48550/arxiv.dg-ga/9503003

34 pages, AMSTeX, no figures

openalex publication_date 1995/03/09 · arxiv created 1996/01/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is the first part of a series of papers. The whole series aims to develop the tools for the study of all almost Hermitian symmetric structures in a unified way. In particular, methods for the construction of invariant operators, their classification and the study of their properties will be worked out. In this paper we present the invariant differentiation with respect to a Cartan connection and we expand the differentials in the terms of the underlying linear connections belonging to the structures in question. Then we discuss the holonomic and non-holonomic jet extensions and we suggest methods for the construction of invariant operators.

Cited by

• Ricci-corrected derivatives and invariant differential operators

Related

• Invariant operators on manifolds with almost Hermitian symmetric structures, II. Normal Cartan connections
• Invariant operators on manifolds with almost Hermitian symmetric structures, III. Standard operators
• More Differential Operators on Almost Hermitian Manifolds
• Some haracterizations of almost Hermitian manifolds
• Homogeneous almost complex structures in dimension 6 with semi-simple isotropy