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In this article we show how certain geometric structures which are also associated with a smooth surface evolve as the shape of the surface changes in a 1-parameter family. We concentrate on the parabolic set and its image under the Gauss map, but the same techniques also classify the changes in the dual of the surface. All these have significance for(More)
The ridge lines on a surface can be defined either via contact of the surface with spheres, or via extrema of principal curvatures along lines of curvature. Certain subsets of ridge lines called crest lines have been singled out by some authors for medical imaging applications. There is a related concept of sub-parabolic line on a surface, also defined via(More)
The reproduction biology of Caspian vimba, Vimba vimba (L.), was investigated on the southwestern coast of the Caspian Sea using 712 fish specimens collected at three fisheries catch stations located in Talesh, Anzali, and Kiashahr over a two-year period from April 2012 through June 2013. Seasonal changes in the gonadosomatic index, gonad histological(More)
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