The geometry of modified Riemannian extensions
We show that every paracomplex space form is locally isometric to a modified Riemannian extension and gives necessary and sufficient conditions for a modified Riemannian extension to be Einstein. We exhibit Riemannian extension Osserman manifolds of signature (3, 3), whose Jacobi operators have non-...
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| Published in: | Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Vol. 465; no. 2107; pp. 2023 - 2040 |
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| Language: | English |
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| Abstract | We show that every paracomplex space form is locally isometric to a modified Riemannian extension and gives necessary and sufficient conditions for a modified Riemannian extension to be Einstein. We exhibit Riemannian extension Osserman manifolds of signature (3, 3), whose Jacobi operators have non-trivial Jordan normal form and which are not nilpotent. We present new four-dimensional results in Osserman geometry. |
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| AbstractList | We show that every paracomplex space form is locally isometric to a modified Riemannian extension and gives necessary and sufficient conditions for a modified Riemannian extension to be Einstein. We exhibit Riemannian extension Osserman manifolds of signature (3, 3), whose Jacobi operators have non-trivial Jordan normal form and which are not nilpotent. We present new four-dimensional results in Osserman geometry. We show that every paracomplex space form is locally isometric to a modified Riemannian extension and gives necessary and sufficient conditions for a modified Riemannian extension to be Einstein. We exhibit Riemannian extension Osserman manifolds of signature (3, 3), whose Jacobi operators have non-trivial Jordan normal form and which are not nilpotent. We present new four-dimensional results in Osserman geometry. |
| Author | García-Río, E. Vázquez-Lorenzo, R. Calviño-Louzao, E. Gilkey, P. |
| Author_xml | – sequence: 1 fullname: E. Calviño-Louzao – sequence: 2 fullname: E. García-Río – sequence: 3 fullname: P. Gilkey – sequence: 4 fullname: R. Vázquez-Lorenzo |
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| References | e_1_3_2_27_1 Hitchin N. (e_1_3_2_28_1) 1990; 124 e_1_3_2_29_1 e_1_3_2_20_1 e_1_3_2_21_1 e_1_3_2_22_1 e_1_3_2_23_1 e_1_3_2_24_1 e_1_3_2_25_1 e_1_3_2_26_1 e_1_3_2_16_1 e_1_3_2_39_1 e_1_3_2_9_1 e_1_3_2_17_1 e_1_3_2_38_1 e_1_3_2_8_1 e_1_3_2_18_1 e_1_3_2_7_1 e_1_3_2_19_1 e_1_3_2_2_1 e_1_3_2_31_1 e_1_3_2_30_1 e_1_3_2_10_1 e_1_3_2_33_1 e_1_3_2_11_1 e_1_3_2_32_1 e_1_3_2_6_1 e_1_3_2_12_1 e_1_3_2_35_1 e_1_3_2_5_1 e_1_3_2_13_1 e_1_3_2_34_1 e_1_3_2_4_1 e_1_3_2_14_1 e_1_3_2_37_1 e_1_3_2_3_1 e_1_3_2_15_1 e_1_3_2_36_1 |
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| Snippet | We show that every paracomplex space form is locally isometric to a modified Riemannian extension and gives necessary and
sufficient conditions for a modified... We show that every paracomplex space form is locally isometric to a modified Riemannian extension and gives necessary and sufficient conditions for a modified... |
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| SubjectTerms | Affine Connection Coordinate systems Curvature Eigenvalues Einstein Geometry Jacobi Operator Mathematical theorems Modified Riemannian Extension Osserman Manifold Para-Kaehler Riemann manifold Signatures Symmetry Tensors |
| Title | The geometry of modified Riemannian extensions |
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