We study quadric surfaces in Euclidean 3-space with non-degenerate second fundamental form, and classify them in terms of the Gaussian curvature, the mean curvature, the second Gaussian curvature and the second mean curvature.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap107-1-4, author = {Dae Won Yoon and Y\i lmaz Tun\c cer and Murat Kemal Karacan}, title = {Non-degenerate quadric surfaces of Weingarten type}, journal = {Annales Polonici Mathematici}, volume = {107}, year = {2013}, pages = {59-69}, zbl = {1263.53007}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap107-1-4} }
Dae Won Yoon; Yılmaz Tunçer; Murat Kemal Karacan. Non-degenerate quadric surfaces of Weingarten type. Annales Polonici Mathematici, Tome 107 (2013) pp. 59-69. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap107-1-4/