Zobrazeno 1 - 10
of 11
pro vyhledávání: '"Alexei Kovalev"'
Autor:
Alexei Kovalev
Publikováno v:
Lectures and Surveys on G2-Manifolds and Related Topics ISBN: 9781071605769
We review some results concerning the deformations of calibrated minimal submanifolds which occur in Riemannian manifolds with special holonomy. The calibrated submanifolds are assumed compact with a non-empty boundary which is constrained to move in
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2ed65a2253d0070b8fa4e96f7c545f86
https://doi.org/10.1007/978-1-0716-0577-6_16
https://doi.org/10.1007/978-1-0716-0577-6_16
Autor:
Alexei Kovalev
Publikováno v:
Lectures and Surveys on G2-Manifolds and Related Topics ISBN: 9781071605769
We explain the constructions for two geometrically different classes of examples of compact Riemannian 7-manifolds with holonomy \(G_2\). One method uses resolutions of singularities of appropriately chosen 7-dimensional orbifolds, with the help of a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a6195b4202c8356fc431b0289903b09c
https://doi.org/10.1007/978-1-0716-0577-6_2
https://doi.org/10.1007/978-1-0716-0577-6_2
We construct a compact formal 7-manifold with a closed $G_2$-structure and with first Betti number $b_1=1$, which does not admit any torsion-free $G_2$-structure, that is, it does not admit any $G_2$-structure such that the holonomy group of the asso
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::831ae98c9b4220d13327c35b7dd37af6
Autor:
Johannes Nordström, Alexei Kovalev
Publikováno v:
Annals of Global Analysis and Geometry. 38:221-257
We construct examples of exponentially asymptotically cylindrical Riemannian 7-manifolds with holonomy group equal to G_2. To our knowledge, these are the first such examples. We also obtain exponentially asymptotically cylindrical coassociative cali
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f0d7f9a072ef28dc23a6e65d3fc1dc5f
https://doi.org/10.1007/s10455-010-9210-8
https://doi.org/10.1007/s10455-010-9210-8
Autor:
M. A. Singer, Alexei Kovalev
Publikováno v:
Geometric And Functional Analysis. 11:1229-1281
1.1 Summary. One of the special features of 4-dimensional differential geometry is the existence of objects with self-dual (SD) or anti-self-dual (ASD) curvature. The objects in question can be connections in an auxiliary bundle over a 4-manifold, le
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5ab2f03be95921f1e1200881ce1ffc6c
https://doi.org/10.1007/s00039-001-8230-8
https://doi.org/10.1007/s00039-001-8230-8
Autor:
Alexei Kovalev, Cyril Proust, Natalia D. Kushch, Luc Brossard, Alain Audouard, M. V. Kartsovnik, David Vignolles
Publikováno v:
Physical Review B. 62:2388-2396
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::666478d741eddd0a3cde3d6835425be2
https://doi.org/10.1103/physrevb.62.2388
https://doi.org/10.1103/physrevb.62.2388
Autor:
Alexei Kovalev
Publikováno v:
The Quarterly Journal of Mathematics. 47:41-58
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::26c02ce13af02dc960901372ed2ebb7d
https://doi.org/10.1093/qjmath/47.185.41
https://doi.org/10.1093/qjmath/47.185.41
Autor:
Alexei Kovalev, Nam-Hoon Lee
We consider the connected-sum method of constructing compact Riemannian 7-manifolds with holonomy G_2 developed in math.DG/0012189. The method requires pairs of projective complex threefolds endowed with anticanonical K3 divisors, the latter `matchin
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cb5d9b54ff792883b0a70cff97d1208b
http://arxiv.org/abs/0810.0957
http://arxiv.org/abs/0810.0957
Autor:
Jason D. Lotay, Alexei Kovalev
Coassociative 4-folds are a particular class of 4-dimensional submanifolds which are defined in a 7-dimensional manifold M with a G_2 structure given by a `positive' differential 3-form, sometimes called G_2-form. Assuming that a G_2-form on M is clo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d5cf2f75f32c8d66a4f093e337dd703d
Autor:
Alexei Kovalev
Publikováno v:
Journal für die reine und angewandte Mathematik (Crelles Journal). 2003
We give a new, connected-sum-like construction of Riemannian metrics with special holonomy G_2 on compact 7-manifolds. The construction is based on a gluing theorem for appropriate elliptic partial differential equations. As a prerequisite, we also o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::47966470851ab63fefd86dc2465666ff
https://doi.org/10.1515/crll.2003.097
https://doi.org/10.1515/crll.2003.097