• Kim, J.S. (Department of Mathematics Education, Sunchon National University) ;
  • Cho, J.H. (Department of Mathematics Education, Sunchon National University) ;
  • Tripathi, M.M. (Department of Mathematics and Astronomy, Lucknow University) ;
  • Prasad, R. (Department of Mathematics and Astronomy, Lucknow University)
  • Published : 2002.10.01


Two examples of $\varepsilon$-famed manifolds are constructed. It is proved that an $\varepsilon$-framed structure on a manifold is not unique. Automorphism groups of r-framed manifolds are studied. Lastly we prove that a connected Lie group G admits a left invariant normal $\varepsilon$-framed structure if and only if the Lie algebra of all left invariant vector fields on G is an $\varepsilon$-framed Lie algebra.


  1. J. Differ-ential Geometry v.4 Geometry of manifolds with structural group u(n)×O(s) D.E. Blair
  2. Lecture Notes in Math. v.509 Contact manifolds in Riemannian geometry
  3. Ann. Univ. Mariae Curie-Sklodowska v.39 no.2 Almost r-paracontact structures A. Bucki;A. Miernowski
  4. J. Math. Soc. Japan v.15 On normal contact structures A. Morimoto
  5. Rend. Mat v.3 no.7 A classification of Riemannian almost-product manifolds A.M. Naveira
  6. Tensor v.30 On a structure similar to almost contact structures I. Sato
  7. Demonstratio Math v.17 On some f(3,ε)-structure manifolds K.D. Singh;Y.N. Singh
  8. Ganita v.40 On normal (e₁,e₂r) ac structure K.D. Singh;M.M. Tripathi
  9. Bulgare Sci. v.26 no.10 Linear connections in an f(3, -1) manifold, Computes Rendus Acad K.D. Singh;R.K. Vohra
  10. Demonstratio Math v.7 no.1 Integrability conditions of (1,1) tensor field f satisfying f³ - f = 0
  11. Kodai Math. Sem. Rep. v.29 The rank of an f-structure R.E. Strong
  12. Demonstratio Math v.29 Almost semi-invariant submanifolds of an ε-framed metric manifold M.M. Tripathi;K.D. Singh
  13. Ann. Scuola Norm. Sup. Pisa Sci. Fis. Mat v.26 Almost r-contact structures J. Vanjura
  14. Tensor v.14 On a structure defined by a tensor field f of type (1,1) satisfying f³ + f = 0 K. Yano
  15. World Scientific Structures on manifold K. Yano;M. Kon