...

  • Home
  • Articles
    • Current Issue
    • Archives
  • Authors
    • Author Guidelines
    • Policies
    • Downloads
  • Editors
  • Reviewers
...

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 47 | Number 5 | Year 2017 | Article Id. IJMTT-V47P547 | DOI : https://doi.org/10.14445/22315373/IJMTT-V47P547

Conformal Geometry of Arc length Functional on Space Curves and Space time


Kulveer Singh Rana, K.C.Petwal
Abstract

The present manuscript is intend to the Quantization of the conformal Arclength functional, Conformal Change of Metric, Conformal geometry of space curve, Conformal structure of two-dimensional spacetimes.

Keywords
Conformal geometry of curves, conformal strings, Griffiths' formalism, linking numbers.
References

[1]. Reese Harvey and Blaine H. Lawson, Calibrated geometries, Acta Math. 148 (1982), 47–157.
[2]. S. Bryson, M. H. Freedman, Z.-X. He, and Z. Wang,
[3]. F. E. Burstall and D. M. J. Calderbank, Conformal submanifold geometry I-III.
[4]. Hiroyuki Tasaki, mass minimizing submanifolds with respect to some Riemannian metrics, J. Math. Soc. Japan 45 (1993), 77–87.
[5]. G. Cairns, R. W. Sharpe, and L. Webb, Conformal invariants for curves and surfaces in three dimensional space forms, Rocky Mountain J. Math. 24 (1994), 933-954.
[6]. E. Musso, The conformal arclength functional, Math. Nachr. 165 (1994), 107-131.
[7]. G. Mari-Beffa, Poisson brackets associated to the Conformal geometry of curves, Trans. Amer. Math. Soc. 357 (2005), 2799-2827.
[8]. R. Langevin and J. O'Hara, Conformally invariant energies of knots, J. Inst. Math. Jussieu 4 (2005), no. 2, 219-280.
[9]. R. Langevin and J. O'Hara, Conformal arc-length as 1, 2 -dimensional length of the set of osculating circles, Comment. Math. Helv. 85 (2010), no. 2, 273-312.
[10]. M. Magliaro, L. Mari, and M. Rigoli, On the geometry of curves and conformal geodesics in the
[11]. M. Eastwood and G. M., Geometric Poisson brackets on Grassmannians and conformal spheres, Proc. Roy. Soc. Edinburgh Sect. A 142 (2012), no. 3, 525-561.
[12]. S. Ourselin and M. A. Styner (eds.), Medical Imaging 2014: Image Processing, Proceedings of SPIE, vol. 9034; doi: 10.1117/12.2052780
[13]. Emilio Musso and Lorenzo Nicolodi, Quantization of the conformal arclength functional on the space curves arXiv:1501.04101v1 [math.DG] (2015).
[14]. Do-Hyung Kim, Causal and conformal structures of globally hyperbolic spacetimes arXiv:1501.06979v1 [math.DG] 2015.
[15]. Do-Hyung Kim, Causal and conformal structures of globally hyperbolic spacetimes arXiv:1501.06979v1 [math.DG] 2015.

Citation :

Kulveer Singh Rana, K.C.Petwal, "Conformal Geometry of Arc length Functional on Space Curves and Space time," International Journal of Mathematics Trends and Technology (IJMTT), vol. 47, no. 5, pp. 338-345, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V47P547

  • PDF
  • Abstract
  • Keywords
  • References
  • Citation
Abstract Keywords References Citation
  • Home
  • Authors Guidelines
  • Paper Submission
  • APC
  • Archives
  • Downloads
  • Open Access
  • Publication Ethics
  • Copyrights Infringement
  • Journals
  • FAQ
  • Contact Us

Follow Us

Copyright © 2025 Seventh Sense Research Group® . All Rights Reserved