Neifeld’s Connection Inducedon the Grassmann Manifold

summary:The work concerns to investigations in the field of differential geometry. It is realized by a method of continuations and scopes of G. F. Laptev which generalizes a moving frame method and Cartan’s exterior forms method and depends on calculation of exterior differential forms. The Grassman...

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Main Author: Belova, Olga
Format: Text
Language:English
Published: Palacký University Olomouc 2016
Subjects:
keyword:Projective space
keyword:the Grassmann manifold
keyword:principal fiber bundle
keyword:Neifeld’s connection
msc:53A20
msc:53B25
laptev
Online Access:http://hdl.handle.net/10338.dmlcz/145811
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record_format openpolar
spelling ftdmlcz:oai:oai.dml.cz:10338.dmlcz/145811 2023-06-11T04:13:49+02:00 Neifeld’s Connection Inducedon the Grassmann Manifold Belova, Olga 2016 application/pdf http://hdl.handle.net/10338.dmlcz/145811 eng eng Palacký University Olomouc issn:0231-9721 mr:MR3674594 zbl:Zbl 1365.53017 reference:[1] Belova, O.: Connections in fiberings associated with the Grassmann manifold and the space of centred planes. J. Math. Sci. 162, 5 (2009), 605–632. MR 2475594, 10.1007/s10958-009-9649-y reference:[2] Borisenko, A. A., Nikolaevskii, Yu. A.: Grassmann’s manifolds and Grassmanian image of the submanifolds. Succ. Math. Sci. 46, 2 (1991), 41–83 (in Russian). MR 1125272 reference:[3] Bortolotti, E.: Connessioni nelle varieta luogo di spazi. Rend. Semin. Fac. Sci. Univ. Cagliari 3 (1933), 81–89. Zbl 0007.36604 reference:[4] Laptev, G. F.: Differential geometry of the embeded manifolds. Proc. Moscow Math. Soc. 2 (1953), 275–383 (in Russian). MR 0057601 reference:[5] Malakhaltsev, M. A.: About internal geometry of Neifeld’s connection. Proc. Moscow Math. Soc. 2 (1986), 67–69 (in Russian). MR 0842329 reference:[6] Neifeld, E. G.: Affine connections on the normalized manifold of planes in the projective space. Proc. Moscow Math. Soc. 11 (1976), 48–55 (in Russian). MR 0487828 reference:[7] Norden, A. P.: The theory of compositions. In: Problemy Geometrii. Itogi Nauki i Tekhniki 10, VINITI, Moscow, 1978, 117–145 (in Russian). MR 0540265 reference:[8] Norden, A. P.: Projective metrics on Grassmann manifolds. News of High Schools, Math. 11 (1981), 80–83 (in Russian). Zbl 0498.53012, MR 0662349 reference:[9] Shevchenko, Yu. I.: Equipments of centreprojective manifolds. Kaliningrad, 2000 (in Russian). access:Unrestricted rights:DML-CZ Czech Digital Mathematics Library, http://dml.cz/ rights:Institute of Mathematics AS CR, http://www.math.cas.cz/ conditionOfUse:http://dml.cz/use keyword:Projective space keyword:the Grassmann manifold keyword:principal fiber bundle keyword:Neifeld’s connection msc:53A20 msc:53B25 type:math text:not_categorized 2016 ftdmlcz 2023-04-24T16:27:34Z summary:The work concerns to investigations in the field of differential geometry. It is realized by a method of continuations and scopes of G. F. Laptev which generalizes a moving frame method and Cartan’s exterior forms method and depends on calculation of exterior differential forms. The Grassmann manifold (space of all $m$-planes) is considered in the $n$-dimensional projective space $P_n$. Principal fiber bundle of tangent linear frames is arised above this manifold. Typical fiber of the principal fiber bundle is the linear group working in the tangent space to the Grassmann manifold. Neifeld’s connection is given in this fibering. It is proved by Cartan’s external forms method, that Bortolotti’s clothing of the Grassmann manifold induces this connection. Text laptev DML-CZ (Czech Digital Mathematics Library)
institution Open Polar
collection DML-CZ (Czech Digital Mathematics Library)
op_collection_id ftdmlcz
language English
topic keyword:Projective space
keyword:the Grassmann manifold
keyword:principal fiber bundle
keyword:Neifeld’s connection
msc:53A20
msc:53B25
spellingShingle keyword:Projective space
keyword:the Grassmann manifold
keyword:principal fiber bundle
keyword:Neifeld’s connection
msc:53A20
msc:53B25
Belova, Olga
Neifeld’s Connection Inducedon the Grassmann Manifold
topic_facet keyword:Projective space
keyword:the Grassmann manifold
keyword:principal fiber bundle
keyword:Neifeld’s connection
msc:53A20
msc:53B25
description summary:The work concerns to investigations in the field of differential geometry. It is realized by a method of continuations and scopes of G. F. Laptev which generalizes a moving frame method and Cartan’s exterior forms method and depends on calculation of exterior differential forms. The Grassmann manifold (space of all $m$-planes) is considered in the $n$-dimensional projective space $P_n$. Principal fiber bundle of tangent linear frames is arised above this manifold. Typical fiber of the principal fiber bundle is the linear group working in the tangent space to the Grassmann manifold. Neifeld’s connection is given in this fibering. It is proved by Cartan’s external forms method, that Bortolotti’s clothing of the Grassmann manifold induces this connection.
format Text
author Belova, Olga
author_facet Belova, Olga
author_sort Belova, Olga
title Neifeld’s Connection Inducedon the Grassmann Manifold
title_short Neifeld’s Connection Inducedon the Grassmann Manifold
title_full Neifeld’s Connection Inducedon the Grassmann Manifold
title_fullStr Neifeld’s Connection Inducedon the Grassmann Manifold
title_full_unstemmed Neifeld’s Connection Inducedon the Grassmann Manifold
title_sort neifeld’s connection inducedon the grassmann manifold
publisher Palacký University Olomouc
publishDate 2016
url http://hdl.handle.net/10338.dmlcz/145811
genre laptev
genre_facet laptev
op_relation issn:0231-9721
mr:MR3674594
zbl:Zbl 1365.53017
reference:[1] Belova, O.: Connections in fiberings associated with the Grassmann manifold and the space of centred planes. J. Math. Sci. 162, 5 (2009), 605–632. MR 2475594, 10.1007/s10958-009-9649-y
reference:[2] Borisenko, A. A., Nikolaevskii, Yu. A.: Grassmann’s manifolds and Grassmanian image of the submanifolds. Succ. Math. Sci. 46, 2 (1991), 41–83 (in Russian). MR 1125272
reference:[3] Bortolotti, E.: Connessioni nelle varieta luogo di spazi. Rend. Semin. Fac. Sci. Univ. Cagliari 3 (1933), 81–89. Zbl 0007.36604
reference:[4] Laptev, G. F.: Differential geometry of the embeded manifolds. Proc. Moscow Math. Soc. 2 (1953), 275–383 (in Russian). MR 0057601
reference:[5] Malakhaltsev, M. A.: About internal geometry of Neifeld’s connection. Proc. Moscow Math. Soc. 2 (1986), 67–69 (in Russian). MR 0842329
reference:[6] Neifeld, E. G.: Affine connections on the normalized manifold of planes in the projective space. Proc. Moscow Math. Soc. 11 (1976), 48–55 (in Russian). MR 0487828
reference:[7] Norden, A. P.: The theory of compositions. In: Problemy Geometrii. Itogi Nauki i Tekhniki 10, VINITI, Moscow, 1978, 117–145 (in Russian). MR 0540265
reference:[8] Norden, A. P.: Projective metrics on Grassmann manifolds. News of High Schools, Math. 11 (1981), 80–83 (in Russian). Zbl 0498.53012, MR 0662349
reference:[9] Shevchenko, Yu. I.: Equipments of centreprojective manifolds. Kaliningrad, 2000 (in Russian).
op_rights access:Unrestricted
rights:DML-CZ Czech Digital Mathematics Library, http://dml.cz/
rights:Institute of Mathematics AS CR, http://www.math.cas.cz/
conditionOfUse:http://dml.cz/use
_version_ 1768391188305412096

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