Reducible Riemannian manifolds with conformal product structures

Key Points

The study reveals that compact reducible Riemannian manifolds can be either conformally flat or structured as triple products.
Under specific technical assumptions, the underlying Riemannian manifolds can be classified into two distinct types.
This research provides key insights into the nature of conformal product structures in the context of Riemannian geometry.
Understanding these geometric structures can lead to new developments in the field of differential geometry.

Abstract

We study conformal product structures on compact reducible Riemannian manifolds, and show that under a suitable technical assumption, the underlying Riemannian mani\-folds are either conformally flat, or triple products, i. e. locally isometric to Riemannian manifolds of the form (M, g) with M=M₁ M₂ M₃ and g=e^2fg₁+g₂+g₃, where gᵢ is a Riemannian metric on Mᵢ, for i\1, 2, 3\, and f C^ (M₁ M₂).

Read Full Paperexternally

Mark Helpful

Bookmark

Relay

View Full Paper

Cite This Study

Moroianu et al. (Sun,) studied this question.

synapsesocial.com/papers/68da58e0c1728099cfd1175e https://doi.org/https://doi.org/10.48550/arxiv.2505.19132