Reduced L q,p -Cohomology of Some Twisted Products
Annales mathématiques Blaise Pascal, Volume 23 (2016) no. 2, pp. 151-169.

Vanishing results for reduced L q,p -cohomology are established in the case of twisted products, which are a generalization of warped products. Only the case qp is considered. This is an extension of some results by Gol ' dshtein, Kuz ' minov and Shvedov about the L p -cohomology of warped cylinders. One of the main observations is the vanishing of the “middle-dimensional” cohomology for a large class of manifolds.

On établit des résultats d’annulation de la cohomologie L q,p réduite pour les produits twistés, une généralisation des produits tordus dans le cas de qp. Le résultats obtenus sont des généralisations de certains résultats par Gol ' dshtein, Kuz ' minov et Shvedov sur la cohomologie L p des cylindres tordus. Une des observations principales est la trivialité de la cohomolgie en dimension “moyenne” pour une large classe de variétés.

DOI: 10.5802/ambp.359
Classification: 58A10, 58A12
Keywords: differential form, reduced $L_{q,p}$-cohomology, twisted cylinder
Vladimir Golʼdshtein 1; Yaroslav Kopylov 2, 3

1 Department of Mathematics Ben Gurion University of the Negev P.O.B. 653 Beer Sheva 84105, Israel
2 Novosibirsk State University ul. Pirogova 2 630090, Novosibirsk, Russia
3 Sobolev Institute of Mathematics Pr. Akad. Koptyuga 4 630090, Novosibirsk, Russia
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Vladimir Golʼdshtein; Yaroslav Kopylov. Reduced $L_{q,p}$-Cohomology of Some Twisted Products. Annales mathématiques Blaise Pascal, Volume 23 (2016) no. 2, pp. 151-169. doi : 10.5802/ambp.359.

[1] Richard L. Bishop; Barrett O’Neill Manifolds of negative curvature, Trans. Am. Math. Soc., Volume 145 (1969), pp. 1-49 | DOI

[2] A. Boulal; Nour El Houda Djaa; Mustapha Djaa; Seddik Ouakkas Harmonic maps on generalized warped product manifolds, Bull. Math. Anal. Appl., Volume 4 (2012) no. 1, pp. 156-165

[3] A. Boulal; Nour El Houda Djaa; A. Zagane Generalized warped product manifolds and biharmonic maps, Acta Math. Univ. Comen. New Ser., Volume 81 (2012) no. 2, pp. 283-298

[4] Bang-yen Chen Geometry of Submanifolds and Its Applications, Science University of Tokyo, Tokyo, 1981, iii+96 pages

[5] Maria Falcitelli A class of almost contact metric manifolds and double-twisted products, Math. Sci. Appl. E-Notes, Volume 1 (2013) no. 1, pp. 36-57

[6] Manuel Fernández-López; Eduardo García-Río; Demir N. Kupeli; Bülent Ünal A curvature condition for a twisted product to be a warped product, Manuscr. Math., Volume 106 (2001) no. 2, pp. 213-217 | DOI

[7] Vladimir M. Golʼdshtejn; Vladimir I. Kuzʼminov; Igor A. Shvedov Reduced L p -cohomology of warped cylinders, Sib. Math. J., Volume 31 (1990) no. 5, pp. 716-727 | DOI

[8] Vladimir M. Golʼdshtejn; Marc Troyanov Sobolev inequalities for differential forms and L q,p -cohomology, J. Geom. Anal., Volume 16 (2006) no. 4, pp. 597-632 | DOI

[9] Vladimir M. Golʼdshtejn; Marc Troyanov The Hölder–Poincaré duality for L q,p -cohomology, Ann. Global Anal. Geom., Volume 41 (2012) no. 1, pp. 25-45 | DOI

[10] Byung Hak Kim; Seoung Dal Jung; Tae Ho Kang; Hong Kyung Pak Conformal transformations in a twisted product space, Bull. Korean Math. Soc., Volume 42 (2005) no. 1, pp. 5-15 | DOI

[11] Yaroslav Kopylov L p,q -cohomology and normal solvability, Arch. Math., Volume 89 (2007) no. 1, pp. 87-96 | DOI

[12] Vladimir I. Kuzʼminov; Igor A. Shvedov On normal solvability of the exterior differentiation on a warped cylinder, Sib. Math. J., Volume 34 (1993) no. 1, pp. 73-82 | DOI

[13] Vladimir I. Kuzʼminov; Igor A. Shvedov On normal solvability of the operator of exterior derivation on warped products, Sib. Math. J., Volume 37 (1996) no. 2, pp. 276-287 | DOI

[14] Ralf Ponge; Helmut Reckziegel Twisted products in pseudo-Riemannian geometry, Geom. Dedicata, Volume 48 (1993) no. 1, pp. 15-25 | DOI

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