On totally contact umbilical submanifolds of a manifold with a sasakian 3-structure

In our paper [5] we proved that any totally contact umbilical submanifold M of a manifold with a Sasakian 3-structure with dim <IMG SRC="http:/img/fbpe/rtfiuz/v27n3/art04ec1.gif" WIDTH=18 HEIGHT=18>> 1, <FONT FACE=Symbol>"</FONT>x<FONT FACE=Symbol>Î</FONT...

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Main Author: Constantin Calin
Format: Article
Language:English
Published: Universidad del Zulia 2004-12-01
Series:Revista Técnica de la Facultad de Ingeniería
Subjects:
Online Access:http://wwww.scielo.org.ve/scielo.php?script=sci_arttext&pid=S0254-07702004000300004
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spelling doaj-9b3c915c7b7d4fa18248decfc628f9ed2020-12-02T03:25:02ZengUniversidad del ZuliaRevista Técnica de la Facultad de Ingeniería0254-07702004-12-01273168172On totally contact umbilical submanifolds of a manifold with a sasakian 3-structureConstantin CalinIn our paper [5] we proved that any totally contact umbilical submanifold M of a manifold with a Sasakian 3-structure with dim <IMG SRC="http:/img/fbpe/rtfiuz/v27n3/art04ec1.gif" WIDTH=18 HEIGHT=18>> 1, <FONT FACE=Symbol>"</FONT>x<FONT FACE=Symbol>Î</FONT>M , is totally contact geodesic. In the present paper we solve the remaining cases. Namely, when dim <IMG SRC="http:/img/fbpe/rtfiuz/v27n3/art04ec1.gif" WIDTH=18 HEIGHT=18 > or = 0, or dim <IMG SRC="http:/img/fbpe/rtfiuz/v27n3/art04ec1.gif" WIDTH=18 HEIGHT=18 > or = 1, M is totally contact geodesic or an intrinsic sphere respectively.<br>En nuestro trabajo [5] probamos que cualquier subvariedad con contacto umbilical completo de una variedad con una estructura-3 Sasakian con dim <IMG SRC="http:/img/fbpe/rtfiuz/v27n3/art04ec1.gif" WIDTH=18 HEIGHT=18>> 1, para todo x que pertenece a M, es de contacto geodésico total. En el presente trabajo resolvemos los casos restantes. A saber, cuando dim <IMG SRC="http:/img/fbpe/rtfiuz/v27n3/art04ec1.gif" WIDTH=18 HEIGHT=18 > o = 0 ó dim <IMG SRC="http:/img/fbpe/rtfiuz/v27n3/art04ec1.gif" WIDTH=18 HEIGHT=18 > o = 1, M es de contacto geodésico total o una esfera intrínseca. rectivamente.http://wwww.scielo.org.ve/scielo.php?script=sci_arttext&pid=S0254-07702004000300004Estructura 3-Sasakiancontacto umbilical completocontacto geodésico totalesfera extrínsecaSasakian-3 structuretotally contact umbilicaltotally contact geodesicextrinsic sphere
collection DOAJ
language English
format Article
sources DOAJ
author Constantin Calin
spellingShingle Constantin Calin
On totally contact umbilical submanifolds of a manifold with a sasakian 3-structure
Revista Técnica de la Facultad de Ingeniería
Estructura 3-Sasakian
contacto umbilical completo
contacto geodésico total
esfera extrínseca
Sasakian-3 structure
totally contact umbilical
totally contact geodesic
extrinsic sphere
author_facet Constantin Calin
author_sort Constantin Calin
title On totally contact umbilical submanifolds of a manifold with a sasakian 3-structure
title_short On totally contact umbilical submanifolds of a manifold with a sasakian 3-structure
title_full On totally contact umbilical submanifolds of a manifold with a sasakian 3-structure
title_fullStr On totally contact umbilical submanifolds of a manifold with a sasakian 3-structure
title_full_unstemmed On totally contact umbilical submanifolds of a manifold with a sasakian 3-structure
title_sort on totally contact umbilical submanifolds of a manifold with a sasakian 3-structure
publisher Universidad del Zulia
series Revista Técnica de la Facultad de Ingeniería
issn 0254-0770
publishDate 2004-12-01
description In our paper [5] we proved that any totally contact umbilical submanifold M of a manifold with a Sasakian 3-structure with dim <IMG SRC="http:/img/fbpe/rtfiuz/v27n3/art04ec1.gif" WIDTH=18 HEIGHT=18>> 1, <FONT FACE=Symbol>"</FONT>x<FONT FACE=Symbol>Î</FONT>M , is totally contact geodesic. In the present paper we solve the remaining cases. Namely, when dim <IMG SRC="http:/img/fbpe/rtfiuz/v27n3/art04ec1.gif" WIDTH=18 HEIGHT=18 > or = 0, or dim <IMG SRC="http:/img/fbpe/rtfiuz/v27n3/art04ec1.gif" WIDTH=18 HEIGHT=18 > or = 1, M is totally contact geodesic or an intrinsic sphere respectively.<br>En nuestro trabajo [5] probamos que cualquier subvariedad con contacto umbilical completo de una variedad con una estructura-3 Sasakian con dim <IMG SRC="http:/img/fbpe/rtfiuz/v27n3/art04ec1.gif" WIDTH=18 HEIGHT=18>> 1, para todo x que pertenece a M, es de contacto geodésico total. En el presente trabajo resolvemos los casos restantes. A saber, cuando dim <IMG SRC="http:/img/fbpe/rtfiuz/v27n3/art04ec1.gif" WIDTH=18 HEIGHT=18 > o = 0 ó dim <IMG SRC="http:/img/fbpe/rtfiuz/v27n3/art04ec1.gif" WIDTH=18 HEIGHT=18 > o = 1, M es de contacto geodésico total o una esfera intrínseca. rectivamente.
topic Estructura 3-Sasakian
contacto umbilical completo
contacto geodésico total
esfera extrínseca
Sasakian-3 structure
totally contact umbilical
totally contact geodesic
extrinsic sphere
url http://wwww.scielo.org.ve/scielo.php?script=sci_arttext&pid=S0254-07702004000300004
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