We study the pseudoriemannian geometry of almost parahermitian manifolds, obtaining a formula for the Ricci tensor of the Levi–Civita connection. The formula uses the intrinsic torsion of an underlying SL(n,ℝ)-structure; we express it in terms of exterior derivatives of some appropriately defined differential forms. As an application, we construct Einstein and Ricci-flat examples on Lie groups. We disprove the parakähler version of the Goldberg conjecture and obtain the first compact examples of a non-flat, Ricci-flat nearly parakähler structure. We study the paracomplex analogue of the first Chern class in complex geometry, which obstructs the existence of Ricci-flat parakähler metrics
Conti, D., & Rossi, F. (2018). The Ricci tensor of almost parahermitian manifolds. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 53(4), 467-501 [10.1007/s10455-017-9584-y].
Citazione: | Conti, D., & Rossi, F. (2018). The Ricci tensor of almost parahermitian manifolds. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 53(4), 467-501 [10.1007/s10455-017-9584-y]. | |
Tipo: | Articolo in rivista - Articolo scientifico | |
Carattere della pubblicazione: | Scientifica | |
Presenza di un coautore afferente ad Istituzioni straniere: | No | |
Titolo: | The Ricci tensor of almost parahermitian manifolds | |
Autori: | Conti, D; Rossi, F | |
Autori: | ROSSI, FEDERICO ALBERTO (Corresponding) | |
Data di pubblicazione: | 2018 | |
Lingua: | English | |
Rivista: | ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s10455-017-9584-y | |
Appare nelle tipologie: | 01 - Articolo su rivista |
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