A Note on Invariance for One Form on Smooth Manifolds

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2017 by IJMTT Journal
Volume-52 Number-4
Year of Publication : 2017
Authors : Dr .S. N. BANASODE, JAYASHREE .S. RADDER, SEEMA B PATIL
  10.14445/22315373/IJMTT-V52P540

MLA

Dr .S. N. BANASODE, JAYASHREE .S. RADDER, SEEMA B PATIL"A Note on Invariance for One Form on Smooth Manifolds", International Journal of Mathematics Trends and Technology (IJMTT). V52(4):267-268 December 2017. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
In this paper we have considered the natural invariance associated with one forms on smooth manifolds and developed proposition on orthonormal frames transformation from one frame to the other.

Reference
[1]Akivis, M.A., and V.V.Goldberg,Projective Differential Geometry of S ubmanifolds,North –Holland Publishing Co.,Amsterdam,1993,xii+362pp.(MR 94i:53001;Zbl.865.53013.)
[2] Akivis, M.A., and V.V.Goldberg,On the structure of submanifolds with degenerate Gauss maps.Goem.Dedicata 86 (2001),no.1-3,205-226.(MR 2003a:53014.)
[3] Akivis, M.A., and V.V.Goldberg,Smooth lines on projective planes over two dimensional algebras,Beitrage Algebra Geom.44 (2003),no.1,165-178.
[4]Nomizu,K., and T. Sasaki, Affine Differential Geometry,Canbridge Tracts in Mathematics, 111,Cambridge University Press,Cambridge,1994,xiv+263pp.(MR 96e:53014;Zbl.834.53002.)

Keywords
orthonormal frames, Euclidean framework, smooth manifolds.