Anti-invariant Riemannian Submersions
P. Gilkey, M. Itoh, and J. H. Park
TL;DR
This paper introduces a Lie-theoretic framework for anti-invariant Riemannian submersions across various geometric structures, providing new examples of Einstein manifolds.
Contribution
It develops a unified Lie-theoretic approach to construct anti-invariant Riemannian submersions for multiple geometric types, expanding the catalog of Einstein manifolds.
Findings
Provides a general construction method for anti-invariant submersions
Generates many compact Einstein examples
Unifies various geometric structures under a common framework
Abstract
We give a general Lie-theoretic construction for anti-invariant almost Hermitian Riemannian submersions, anti-invariant quaternion Riemannian submersions, anti-invariant para-Hermitian Riemannian submersions, anti-invariant para-quaternion Riemannian submersions, and anti-invariant octonian Riemannian submersions. This yields many compact Einstein examples.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds