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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

IMPACT FACTOR 2018: 0.789

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Volume 19, Issue 4


Principal curvatures and parallel surfaces of wave fronts

Keisuke Teramoto
  • Corresponding author
  • Department of Mathematics, Graduate School of Science, Kobe University, Rokko, Kobe 657-8501, Japan
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  • Other articles by this author:
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Published Online: 2019-09-11 | DOI: https://doi.org/10.1515/advgeom-2018-0038


We give criteria for which a principal curvature becomes a bounded C-function at non-degenerate singular points of wave fronts by using geometric invariants. As applications, we study singularities of parallel surfaces and extended distance squared functions of wave fronts. Moreover, we relate these singularities to some geometric invariants of fronts.

Keywords: Principal curvature; singularity; wave front; parallel surface; extended distance squared function

MSC 2010: 57R45; 53A05; 58K05


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About the article

Received: 2017-05-22

Revised: 2017-09-27

Published Online: 2019-09-11

Published in Print: 2019-10-25

Communicated by: P. Eberlein

Funding The author was partly supported by the Grant-in-Aid for JSPS Fellows, No. 17J02151.

Citation Information: Advances in Geometry, Volume 19, Issue 4, Pages 541–554, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2018-0038.

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