Minimal cubic cones via Clifford algebras
2010 (English)In: Complex Analysis and Operator Theory, ISSN 1661-8254, Vol. 4, no 3, 685-700 p.Article in journal (Refereed) Published
In this paper, we construct two infinite families of algebraic minimal cones in R n . The first family consists of minimal cubics given explicitly in terms of the Clifford systems. We show that the classes of congruent minimal cubics are in one to one correspondence with those of geometrically equivalent Clifford systems. As a byproduct, we prove that for any n ≥ 4, n ≠ 16k + 1, there is at least one minimal cone in R n given by an irreducible homogeneous cubic polynomial. The second family consists of minimal cones in R m 2 , m ≥ 2, defined by an irreducible homogeneous polynomial of degree m. These examples provide particular answers to the questions on algebraic minimal cones in R n posed by Wu-Yi Hsiang in the 1960s.
Place, publisher, year, edition, pages
SP Birkhäuser Verlag Basel , 2010. Vol. 4, no 3, 685-700 p.
Minimal submanifolds, Clifford algebras, Clifford systems, Algebraic minimal cones, Primary 53C42, 49Q05, Secondary 53A35
Mathematical Analysis Geometry
IdentifiersURN: urn:nbn:se:liu:diva-79619DOI: 10.1007/s11785-010-0078-1OAI: oai:DiVA.org:liu-79619DiVA: diva2:577358