On a class of submanifolds in tangent bundle with g- natural metric

TL;DR

This paper investigates a specific class of submanifolds within tangent bundles equipped with g-natural metrics, exploring their geometric properties and the implications of isometric immersions.

Contribution

It introduces a new class of submanifolds in tangent bundles with g-natural metrics and analyzes their geometric characteristics.

Findings

Characterization of submanifolds in tangent bundles with g-natural metrics

Conditions for isometric immersions of tangent bundles

Insights into the geometry of tangent bundle submanifolds

Abstract

An isometric immersion of a Riemannian manifold M into a Riemannian manifold N gives rise in a natural way to the immersion of the tangent bundle TM into the tangent bundle TN with a non-degenerate g- natural metric G.