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A Note on Osserman Lorentzian Manifolds
Author(s) -
Blažić Novica,
Bokan Neda,
Gilkey Peter
Publication year - 1997
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609396002238
Subject(s) - mathematics , sectional curvature , manifold (fluid mechanics) , constant (computer programming) , pure mathematics , curvature , mathematical analysis , mean curvature , geometry , scalar curvature , mechanical engineering , computer science , engineering , programming language
Let p be a point of a Lorentzian manifold M . We show that if M is spacelike Osserman at p , then M has constant sectional curvature at p ; similarly, if M is timelike Osserman at p , then M has constant sectional curvature at p . The reverse implications are immediate. The timelike case and 4‐dimensional spacelike case were first studied in [ 3 ]; we use a different approach to this case. 1991 Mathematics Subject Classification 53B30, 53C50.