Jacobi–tsankov Manifolds Which Are Not 2–step Nilpotent
نویسندگان
چکیده
There is a 14-dimensional algebraic curvature tensor which is Jacobi–Tsankov (i.e. J (x)J (y) = J (y)J (x) for all x, y) but which is not 2-step Jacobi nilpotent (i.e. J (x)J (y) 6= 0 for some x, y); the minimal dimension where this is possible is 14. We determine the group of symmetries of this tensor and show that it is geometrically realizable by a wide variety of pseudo-Riemannian manifolds which are geodesically complete and have vanishing scalar invariants. Some of the manifolds in the family are symmetric spaces. Some are 0-curvature homogeneous but not locally homogeneous.
منابع مشابه
Se p 20 06 JACOBI – TSANKOV MANIFOLDS WHICH ARE NOT 2 - STEP NILPOTENT
There is a 14-dimensional algebraic curvature tensor which is Jacobi–Tsankov (i.e. J (x)J (y) = J (y)J (x) for all x, y) but which is not 2-step Jacobi nilpotent (i.e. J (x)J (y) = 0 for some x, y); the minimal dimension where this is possible is 14. We determine the group of symmetries of this tensor and show that it is geometrically realizable by a wide variety of pseudo-Riemannian manifolds ...
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