Carleman estimates for the Laplace-Beltrami equation on complex manifolds
Aldo Andreotti, Edoardo Vesentini (1965)
Publications Mathématiques de l'IHÉS
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Aldo Andreotti, Edoardo Vesentini (1965)
Publications Mathématiques de l'IHÉS
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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.
Paul Gauduchon, Andrew Balas (1985)
Mathematische Zeitschrift
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Roberto Catenacci, Annalisa Marzuoli (1984)
Annales de l'I.H.P. Physique théorique
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Vasile Oproiu, Neculai Papaghiuc (2005)
Colloquium Mathematicae
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In [11] we have considered a family of almost anti-Hermitian structures (G,J) on the tangent bundle TM of a Riemannian manifold (M,g), where the almost complex structure J is a natural lift of g to TM interchanging the vertical and horizontal distributions VTM and HTM and the metric G is a natural lift of g of Sasaki type, with the property of being anti-Hermitian with respect to J. Next, we have studied the conditions under which (TM,G,J) belongs to one of the eight classes of anti-Hermitian...
Erdem, Sadettin (1999)
Serdica Mathematical Journal
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It is shown that the spheres S^(2n) (resp: S^k with k ≡ 1 mod 4) can be given neither an indefinite metric of any signature (resp: of signature (r, k − r) with 2 ≤ r ≤ k − 2) nor an almost paracomplex structure. Further for every given Riemannian metric on an almost para-Hermitian manifold with the associated 2-form φ one can construct an almost Hermitian structure (under certain conditions, two different almost Hermitian structures) whose associated 2-form(s) is φ.
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...
Tshikuna-Matamba, T. (2004)
International Journal of Mathematics and Mathematical Sciences
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