Codimension one isometric immersions between Lorentz spaces
Author:
L. K. Graves
Journal:
Trans. Amer. Math. Soc. 252 (1979), 367392
MSC:
Primary 53C50; Secondary 53C42
MathSciNet review:
534127
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Abstract: The theorem of Hartman and Nirenberg classifies codimension one isometric immersions between Euclidean spaces as cylinders over plane curves. Corresponding results are given here for Lorentz spaces, which are Euclidean spaces with one negativedefinite direction (also known as Minkowski spaces). The pivotal result involves the completeness of the relative nullity foliation of such an immersion. When this foliation carries a nondegenerate metric, results analogous to the HartmanNirenberg theorem obtain. Otherwise, a new description, based on particular surfaces in the threedimensional Lorentz space, is required.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197905341274
PII:
S 00029947(1979)05341274
Keywords:
Lorentz spaces,
isometric immersions,
null curves,
null frames,
relative nullity foliation,
(non)degenerate relative nullities,
complete relative nullities,
HartmanNirenberg theorem,
cylinders over plane curves,
Bscrolls
Article copyright:
© Copyright 1979
American Mathematical Society
