Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Reducibility of isometric immersions
HTML articles powered by AMS MathViewer

by John Douglas Moore PDF
Proc. Amer. Math. Soc. 34 (1972), 229-232 Request permission

Abstract:

For $i = 1,2$, suppose that the connected riemannian manifold ${M_i}$ possesses a codimension ${p_i}$ euclidean isometric immersion whose first normal space has dimension ${p_i}$ and whose type number is at least two at each point, and let $N = \dim ({M_1} \times {M_2}) + {p_1} + {p_2}$. In this note it is proven that if f is any isometric immersion from the riemannian product ${M_1} \times {M_2}$ into euclidean N-space ${E^N}$, then there exists an orthogonal decomposition ${E^N} = {E^{{N_1}}} \times {E^{{N_2}}}$ together with isometric immersions ${f_i}:{M_i} \to {E^{{N_i}}}$ such that $f = {f_1} \times {f_2}$.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53C40
  • Retrieve articles in all journals with MSC: 53C40
Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 34 (1972), 229-232
  • MSC: Primary 53C40
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0293546-3
  • MathSciNet review: 0293546