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Almost analytic forms with respect to a quadratic endomorphism and their cohomology

The goal of this paper is to consider the notion of almost analytic form in a unifying setting for both almost complex and almost paracomplex geometries. We use a global formalism, which yields, in addition to generalizations of the main results of the previously known almost complex case, a relationship with the Frölicher-Nijenhuis theory. A cohomology of almost analytic forms is also introduced and studied as well as deformations of almost analytic forms with pairs of almost analytic functions.

Anahtar Kelimeler:

Quadratic endomorphism, almost $F$-analytic form, $F$-symmetric form, almost (para)complex structure, cohomology

Almost analytic forms with respect to a quadratic endomorphism and their cohomology

Keywords:

Quadratic endomorphism, almost $F$-analytic form, $F$-symmetric form, almost (para)complex structure, cohomology,

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auser, 2010.
Crasmareanu M, Ida C. Almost analyticity on almost (para) complex Lie algebroids. Results in Math 2015 (in press).
Cruceanu V, Fortuny P, Gadea PM. A survey on paracomplex geometry. Rocky Mountain J Math 1996; 26: 83–115.
Gezer A, Cengiz N, Salimov AA. On integrability of golden Riemannian structures. Turk J Math 2013; 37: 693–703.
Iscan M, Salimov AA. On K¨ahler-Norden manifolds. P Indian AS-Math Sci 2009; 119: 71–80.
Kruchkovich GI. Hypercomplex structure on a manifold. Tr Sem Vect Tens Anal Moscow Univ 1972; 16: 174–201.
Petersen P. Riemannian Geometry. Graduate Texts in Mathematics, Vol. 171. 2nd ed. New York, NY, USA: Springer, 200 Pitis G, Smaranda D. Formes presque analytiques sur une vari´et´e presque complexe. Zb Rad Prirod-Mat Fak Ser Mat 1991; 21: 2329 (in French).
Salimov AA, Gezer A. Norden structures of Hessian type. Turk J Math 2014; 38: 462–469.
Salimov AA, Iscan M, Akbulut K. Notes on para-Norden-Walker 4-manifolds. Int J Geom Methods Mod Phys 2010; 7: 1331–1347.
Salimov AA, Iscan M, Etayo F. Paraholomorphic B -manifold and its properties. Topol Appl 2007; 154: 925–933.
Simionescu C, Pitis G. Some properties of almost analytic forms. Bull Univ Brasov Ser C 1989; 31: 75–80.
Smaranda D. The algebra of almost analytic forms and criteria of almost analyticity. In: Special Chapters in Differential Geometry. Bucharest, Romania: University of Bucharest, 1981, pp. 67–87 (in Romanian).
Tachibana S. Analytic tensor and its generalization. Tˆohoku Math J 1960; 12: 208–221.
Tachibana S, Kotˆo S. On almost-analytic functions, tensors and invariant subspaces. Tˆohoku Math J 1962; 14: 177–186.
Yano K. Differential Geometry on Complex and Almost Complex Spaces. International Series of Monographs in Pure and Applied Mathematics, Vol. 49. New York, NY, USA: Pergamon Press, 1965.
Yano K, Ako M. On certain operators associated with tensor fields. Kodai Math Sem Rep 1968; 20: 414–436.
Zamkovoy S. Canonical connections on paracontact manifolds. Ann Glob Anal Geom 2008; 36: 37–60.