A pseudo-inverse of the fundamental form and its application to affine immersions of non-degenerate surfaces

Ryuji Ishii

doi:10.20604/00001058

January 1, 2006Open Access

A pseudo-inverse of the fundamental form and its application to affine immersions of non-degenerate surfaces

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Key Points

This research aims to establish a pseudo-inverse of the fundamental form for affine immersions of non-degenerate surfaces.
Defined a canonical transversal bundle based on the existence of a pseudo-inverse of the fundamental form.
Generalized existing methods for non-degenerate surfaces in R4 to 4-dimensional manifolds with torsion-free connection.
A new framework for transversal bundles in a broader context of geometry was developed.
Successful application of these concepts enhances understanding of non-degenerate surfaces.

Implication

Research demonstrates the construction of transversal bundles for non-degenerate surfaces, indicating broader applications in geometry.

Abstract

We choose a canonical transversal bundle of an affine immersion if a pseudo-inverse of the fundamental form exists.In particular, well-known canonical transversal bundles for a non-degenerate surface in R 4 are generalized to those for a non-degenerate surface in 4-dimensional manifold with torsion-free connection.

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Ryuji Ishii (2006) studied this question.

synapsesocial.com/papers/69cf5c925a333a821460a1e5 https://doi.org/10.20604/00001058

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A pseudo-inverse of the fundamental form and its application to affine immersions of non-degenerate surfaces

Key Points

Implication

Abstract

Discussion

Cite This Study

A pseudo-inverse of the fundamental form and its application to affine immersions of non-degenerate surfaces

Key Points

Implication

Abstract

Discussion

Cite This Study

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