Stochastic perturbation of geodesics on the manifold of Riemannian metrics

Q: What type of study is this?

This is a Quantitative Study study.

Ana Bela Cruzeiro; Ali Suri

doi:10.48550/arxiv.2507.16959

July 22, 2025Open Access

Stochastic perturbation of geodesics on the manifold of Riemannian metrics

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Key Points

The study computes the evolution equation influenced by stochastic perturbation effects on Riemannian metrics.
Using diffusion processes, the research establishes a framework for analyzing Lagrangian dynamics with stochastic characteristics.
The results provide a novel perspective on the interplay between stochastic phenomena and geometric structures.
The findings may have implications for the understanding of complex systems influenced by random fluctuations.

Implication

This study computes the evolution equation for Lagrangian dynamics on Riemannian metrics, highlighting stochastic effects and diffusion processes.

Abstract

In this paper, using diffusion processes, we compute the evolution equation on the manifold of Riemannian metrics for the Lagrangian induced by the L² stochastic kinetic energy functional.

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Cite This Study

Cruzeiro et al. (2025) studied this question.

synapsesocial.com/papers/68e6494525bc5bdb98713a1d https://doi.org/10.48550/arxiv.2507.16959

View Full Paper

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Stochastic perturbation of geodesics on the manifold of Riemannian metrics

Key Points

Implication

Abstract

Discussion

Cite This Study

Stochastic perturbation of geodesics on the manifold of Riemannian metrics

Key Points

Implication

Abstract

Discussion

Cite This Study

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