On the cover problems of geometric theory
Nicos Karcanias, Dimitris Vafiadis (1993)
Kybernetika
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Displaying similar documents to “On the functional independence of scalar invariants of curvature for dimensions n=2,3,4”
On the cover problems of geometric theory
A basic decomposition result related to the notion of the rank of a matrix and applications.
Mortici, Cristinel (2003)
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The nonexistence of rank 4 IP tensors in signature .
Pearson, Kelly Jeanne, Zhang, Tan (2002)
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The maximal and minimal ranks of with applications.
Tian, Yongge, Cheng, Shizhen (2003)
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Forms equivalent to curvatures.
Horacio Porta, Lázaro Recht (1986)
Revista Matemática Iberoamericana
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The 2-forms, Ω and Ω' on a manifold M with values in vector bundles ξ --> M and ξ' --> M are equivalent if there exist smooth fibered-linear maps ξ --> ξ' and W: ξ --> ξ' with Ω' = UΩ and Ω = WΩ'. It is shown that an ordinary 2-form equivalent to the curvature of a linear connection has locally a non-vanishing integrating factor at each point in the interior of the set rank (ω) = 2 or in the set rank (ω) > 2. Under favorable conditions the...
Possible numbers ofx’s in an {x,y}-matrix with a given rank
Chao Ma (2017)
Open Mathematics
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Let x, y be two distinct real numbers. An {x, y}-matrix is a matrix whose entries are either x or y. We determine the possible numbers of x’s in an {x, y}-matrix with a given rank. Our proof is constructive.
Curvature tensors in dimension four which do not belong to any curvature homogeneous space
Oldřich Kowalski, Friedbert Prüfer (1994)
Archivum Mathematicum
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A six-parameter family is constructed of (algebraic) Riemannian curvature tensors in dimension four which do not belong to any curvature homogeneous space. Also a general method is given for a possible extension of this result.