9971

9200

كارشناسي ارشد

رياضي محض ﴿هندسه﴾

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1393

هفت، 64ص.: مصور

ص.ع. به فارسي و انگليسي

اعظم اعتماد

امير هاشمي

94/2/16

محمدرضا كوشش، مهدي نعمتي

1396/09/26

كتابنامه

علوم رياضي

رياضي

ID9200

A survey on Chen inequality for submanifold of some space forms Fahimeh Aboualhasan Beigi fahimeh beygi@gmail com 2014 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Azam Etemad ae110mat@cc iut ac ir Advisor Dr Amir Hashemi Amir Hashemi@cc iut ac ir 2010 MSC 53B15 53B05 53C40 Keywords rst Chen inequality quasi constant space form cosymplectic space form and real space form Abstract One of the problem considered in Riemannian geometry is checking inequalities for submanifolds in various space forms endowed with a semi symmetric metric connection If the torsion tensor Tof linear connection on Riemannian manifold M g satis es T X Y Y X X Y for any vector elds X Y and 1 form then the connection is called a semi symmetric connection If g 0 then is called a semi symmetric metric connection on M Most of these inequalities are toexplained relations between the extrinsic geometry and intrinsic geometry of a submanifold Amongall the submanifold properties mean sectional scalar and Ricci curvatures are usually present in theinequalities The most famous inequalities of the submanifold are Chen inequality In fact the rstChen inequality representer a inequality between scalar curvature and mean curvature The specialform of this inequality is determined by properties of space forms For example a Riemannian manifold M g of quasi constant curvature is a Riemannian manifold with the curvature tensor satisfying in thespecial condition on the curvature tensor Now if and K be scalar curvature and sectional curvatureof M respectively and moreover the rst Chen invariant is de ned by M n p p inf K Tp M n p M n dim 2 then Chen inequality for submanifold of Riemannian manifold of quasi 2constant curvature will be state by M n p n 2 2 n 1 H 2 n 1 a b n 1 P 2 P 2 n 2where P is tangent component of P and P pr P If the vector eld P is tangent or normal to M nthen inequality will change We can observe in this inequality that there is a relation between squared

اعظم اعتماد

امير هاشمي

محمدرضا كوشش، مهدي نعمتي