Some Results on Anti-Invariant Submanifolds of \((LCS)_N\)-Manifold

Authors

  • C. S. Bagewadi Department of Mathematics, Kuvempu University, Shankaraghatta, Shimoga, Karnataka
  • S. Venkatesha Department of Mathematics, Kuvempu University, Shankaraghatta, Shimoga, Karnataka
  • M. S. Siddesha Department of Mathematics, New Horizon College of Engineering, Bangalore

DOI:

https://doi.org/10.26713/jims.v10i4.797

Keywords:

Anti-invariant submanifold, \((LCS)_n\)-manifold, Horizontal and vertical projections, Totally umbilical, Totally geodesic

Abstract

The object of the present paper is to study anti-invariant submanifolds \(M\) of \((LCS)_{n}\)-manifold \(\bar{M}\). The basic equations are decomposed into horizontal and vertical homomorphisms and geometric properties of anti-invariant submanifolds are studied.

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References

S.R. Ashoka, C.S. Bagewadi and G. Ingahhalli, A Geometry on Ricci solitons in ((LCS)_n) manifolds, Differential Geometry-Dynamical Systems 16 (2014), 50 – 62, DOI: http://vectron.mathem.pub.ro/dgds/v16/D16-as-768.pdf.

C.S. Bagewadi, On totally real submanifolds of a Kahlerian manifold addmitting semisymmetric metric connection, Indian J. Pure Appl. Math. 13(5) (1982), 528 – 536, DOI: https://www.insa.nic.in/writereaddata/UpLoadedFiles/IJPAM/20005a7d_528.pdf.

A. Brasil, G.A. Lobos and M. Marlano, C-Totally real submanifolds with parallel mean curvature in (lambda)-Sasakian space forms, Matematica Contemporacnca Sociedade Brasileia de Matematicano, 34(c) (2008), http://mc.sbm.org.br/docs/mc/pdf/34/a5.pdf.

B.Y. Chen, Geometry of Submanifolds and its Applications, Science University of Tokyo, Tokyo (1981).

S.K. Hui and D. Chakraborty, Some types of Ricci Solitons on ((LCS)_n) manifolds, Journal of Mathematical Science Advances and Applications 37 (2016), 1 – 17.

S.K. Hui, M. Ateken and S. Nandy, Contact CR-Wrapped product ((LCS)_n) manifolds, Act. Math. Univ. 1 (xxxv)(1.1) (2017), 101 – 109.

M. Kon, Invariant submanifolds of normal contact metric manifolds, Kodai Math. Sem. Rep. 27 (1973), 330 – 336.

K. Matsumoto, On Lorentzian almost paracontact manifolds with a structure of concircular type, Bull. Yamagata Uni. Natur. Sci. 12 (1989), 151 – 156.

C. Ozgur and C. Murathan, On invariant submanifolds of Lorenzian para-Sasakian manifolds, The Arabian J. Sci. Engg. 34(24) (2009), 177 – 185.

H.B. Pandey and Anilkumar, Anti-invariant Submanifolds of almost para contact manifolds, Indian J. Pure and Appl. Math. 16(6) (1985), 586 – 590, https://www.insa.nic.in/writereaddata/UpLoadedFiles/IJPAM/20005a6a_586.pdf.

G.P. Pokhariyal and R.S. Mishra, Curvature tensors and their relativistics significance, Yokohama Mathematical Journal 18 (1970), 105 – 108, http://hdl.handle.net/11295/38452.

D.G. Prakasha, On Ricci (eta)-recurrent ((LCS)_n)-manifolds, Acta Universitatis Apulensis 24 (2010), 449 – 461, https://www.emis.de/journals/AUA/acta24/Paper-11-Acta24.2010.pdf.

M.H. Shahid, Some results on anti-invariant submanifolds of a trans-Sasakian manifold, Bull. Malays. Math. Sci. 27(2) (2004), 117 – 127.

A.A. Shaikh, On Lorentzian almost paracontact manifolds with a structure of concircular type, Kyungpook Math. J. 43(2) (2003), 305 – 314, https://www.emis.de/journals/BMMSS/pdf/v27n2/ v27n2p3.pdf.

A.A. Shaikh, Some results on ((LCS)_n)-manifolds, J. Korean Math. Soc. 46(3) (2009), 449 – 461, DOI: 10.4134/JKMS.2009.46.3.449.

A.A. Shaikh, T. Basu and S. Eyasmin, On the existence of (phi)-Recurrent ((LCS)_n)-manifolds, Extracta Mathematicae 23(1) (2008), 71 – 83, https://www.eweb.unex.es/eweb/extracta/Vol-23-1/23B1Shai.pdf.

A.A. Shaikh, Y. Matsuyama and S.K. Hui, On invariant submanifolds of ((LCS)_n)-manifolds, Journal of the Egyptian Mathematical Society 24(2) (2016), 263 – 269, DOI: 10.1016/j.joems.2015.05.008.

M.S. Siddesha and C.S. Bagewadi, Submanifold of a ((k,mu))-Contact manifold, CUBO A Mathematical Journal 18(01) (2016), 59 – 68, DOI: https://scielo.conicyt.cl/pdf/cubo/v18n1/art05.pdf.

M.S. Siddesha and C.S. Bagewadi, On some classes of invariant submanifolds ((k,mu))-contact manifold, Journal of Informatics and Mathematical Sciences 9(1) (2017), 13 – 26, DOI: 10.26713/jims.v9i1.451.

M.S. Siddesha, D. Nirmala and C.S. Bagewadi, On invariant submanifolds of Lorentzian (beta)-Kenmotsu manifold, Asian Journal of Mathematics and Computer Research 19(4) (2017), 203 – 213.

S. Sular and C. Ozgur, On some submanifolds of Kenmotsu manifolds, Chaos, Solitons and Fractals 42 (2009), 1990 – 1995, DOI: 10.1016/j.chaos.2009.03.185.

M.M. Tripathi, T. Sasahara and J.S. Kim, On invariant submanifolds of contact metric manifolds, Tsukuba J. Math. 29(2) (2005), 495 – 510, https://www.jstor.org/stable/43686379?seq=1#page_scan_tab_contents.

Venkatesha and C.S. Bagewadi, On concircular (phi)-recurrent LP-Sasakian manifolds, Differ. Geom. Dyn. Syst. 10 (2008), 312 – 319, URL: http://www.mathem.pub.ro/dgds/v10/D10-VE.pdf.

Venkatesha, C.S. Bagewadi and K.T. Pradeep Kumar, Some results on Lorentzian para-Sasakian manifolds, ISRN Geometry 2011 (2011), Article ID 161523, 9 pages, DOI: 10.5402/2011/161523.

K.R. Vidyavathi and C.S. Bagewadi, A study on ((LCS)_n) manifolds admitting (eta)-Ricci soliton, JMI International Journal of Mathematical Science 5 (2017), 47 – 52.

K. Yano, On structure (f)-satisfying (f^3 + f = 0), Technical Report, University of Washington, 12 (1961).

K. Yano, On structure defined by a tensor field of type (1,1) satisfying (f^3+f =0), Tensor 14 (1963), 99 – 109.

K. Yano and M. Kon, Anti-invariant submanifolds of a Sasakian space forms-II, J. Korean Math. Soc. 13 (1976), 1 – 14.

K. Yano and M. Kon, Structures on Manifolds, World Scientific Publishing (1984).

A. Yildz and C. Murathan, Invariant submanifolds of Sasakian space forms, J. Geom. 95 (2009), 135 – 150, DOI: 10.1007/s00022-009-0011-9.

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Published

2018-12-31
CITATION

How to Cite

Bagewadi, C. S., Venkatesha, S., & Siddesha, M. S. (2018). Some Results on Anti-Invariant Submanifolds of \((LCS)_N\)-Manifold. Journal of Informatics and Mathematical Sciences, 10(4), 623–634. https://doi.org/10.26713/jims.v10i4.797

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Research Articles