Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-25T14:51:01.269Z Has data issue: false hasContentIssue false

Subspaces Of Riemannian Spaces

Published online by Cambridge University Press:  20 November 2018

Richard Blum*
Affiliation:
University of Saskatchewan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, results obtained by the author for Riemannian Spaces Vn imbedded in Euclidean Spaces EN (3; 4) are extended to Vn imbedded in VN.

The first section is introductory. In §2 the general result is obtained. This is the establishment of a certain dependency among the three basic sets of equations of the Vn with respect to the VN, namely the equations of Gauss, Codazzi and Kuehne.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1955

References

1. Allendoerfer, C. B., Rigidity for spaces of class greater than one, Am. Journal of Math., 61 (1939), 633644.Google Scholar
2. Blum, R., Anzahl der Identitaeten von Bianchi in einer Vn , Bull. Sect. Sci. Acad. Roumaine. 28 (1946) no. 6.Google Scholar
3. Blum, R., Bedingungsgleichungen einer Vn in einer EN , Bull. Math. Soc. Roum. des Sciences, 47 (1946), 144201.Google Scholar
4. Blum, R., Sur les tenseurs dérivés de Gauss et Codazzi, C. R. Acad. Sci., Paris 224 (1947), 708709.Google Scholar
5. Blum, R., Sur les identités de Bianchi et Veblen, C. R. Acad. Sci., Paris 224 (1947), 889890.Google Scholar
6. Blum, R., Sur la classe des variétées riemanniennest, Bull. Math. Soc. Roum. des Sciences, 48 (1947), 88101.Google Scholar
7. Burstin, C., Ein Beitrag zunt Problem der Einbettung Riemannscher Räume in Euklidische Räume, Math. Sbornik, 38 (1931), 7491.Google Scholar
8. Eisenhart, L. P., Riemannian Geometry (Princeton, 1926).Google Scholar
9. Kuehne, H., Die Grundgleichungen einer beliebigen Mannigfaltigkeitt, Arch. d. Math. u. Phys., 4 (1903), 300311.Google Scholar
10. Thomas, T. Y., Riemannian Spaces of class one and their characterization, Acta Math., 67 (1936), 169211.Google Scholar