Geodesics and Submanifold Structures in Conformal Geometry

Florin Belgun

doi:10.1016/j.geomphys.2015.01.014

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arXiv · 1411.4404

Geodesics and Submanifold Structures in Conformal Geometry

Florin Belgun

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Abstract

A conformal structure on a manifold $M^n$ induces natural second order conformally invariant operators, called M\"obius and Laplace structures, acting on specific weight bundles of $M$, provided that $n\ge 3$. By extending the notions of M\"obius and Laplace structures to the case of surfaces and curves, we develop here the theory of extrinsic conformal geometry for submanifolds, find tensorial invariants of a conformal embedding, and use these invariants to characterize various forms of geodesic submanifolds.

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BibTeX RIS

Florin Belgun. 2014-11-17. Geodesics and Submanifold Structures in Conformal Geometry. https://doi.org/10.1016/j.geomphys.2015.01.014

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