Almost Hermitian structures on the frame bundle of an almost Hermitian manifold
R. Castro, A. Tarrio (1990)
Annales Polonici Mathematici
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R. Castro, A. Tarrio (1990)
Annales Polonici Mathematici
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Simona-Luiza Druţă-Romaniuc (2012)
Czechoslovak Mathematical Journal
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We obtain the natural diagonal almost product and locally product structures on the total space of the cotangent bundle of a Riemannian manifold. Studying the compatibility and the anti-compatibility relations between the determined structures and a natural diagonal metric, we find the Riemannian almost product (locally product) and the (almost) para-Hermitian cotangent bundles of natural diagonal lift type. Finally, we prove the characterization theorem for the natural diagonal (almost)...
Ana Dorotea Tarrío Tobar (1987)
Extracta Mathematicae
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Roberto Catenacci, Annalisa Marzuoli (1984)
Annales de l'I.H.P. Physique théorique
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Vestislav Apostolov, Paul Gauduchon (2002)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We provide a local classification of selfdual Einstein riemannian four-manifolds admitting a positively oriented hermitian structure and characterize those which carry a hyperhermitian, non-hyperkähler structure compatible with the negative orientation. We show that selfdual Einstein 4-manifolds obtained as quaternionic quotients of and are hermitian.
Ruxandra Moraru, Misha Verbitsky (2010)
Open Mathematics
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A hypercomplex manifold is a manifold equipped with three complex structures I, J, K satisfying the quaternionic relations. Let M be a 4-dimensional compact smooth manifold equipped with a hypercomplex structure, and E be a vector bundle on M. We show that the moduli space of anti-self-dual connections on E is also hypercomplex, and admits a strong HKT metric. We also study manifolds with (4,4)-supersymmetry, that is, Riemannian manifolds equipped with a pair of strong HKT-structures...
Francisco Martín Cabrera (1998)
Czechoslovak Mathematical Journal
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We consider almost hyper-Hermitian structures on principal fibre bundles with one-dimensional fiber over manifolds with almost contact 3-structure and study relations between the respective structures on the total space and the base. This construction suggests the definition of a new class of almost contact 3-structure, which we called trans-Sasakian, closely connected with locally conformal quaternionic Kähler manifolds. Finally we give a family of examples of hypercomplex manifolds...