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Minimal Cubic Cones via Clifford Algebras
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2010 (English)In: Complex Analysis and Operator Theory, ISSN 1661-8254, Vol. 4, no 3, 685-700 p.Article in journal (Refereed) Published
Abstract [en]

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 not equal 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-m2, 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
2010. Vol. 4, no 3, 685-700 p.
Keyword [en]
Minimal submanifolds, Clifford algebras, Clifford systems, Algebraic minimal cones
National Category
URN: urn:nbn:se:kth:diva-26698DOI: 10.1007/s11785-010-0078-1ISI: 000281904100009ScopusID: 2-s2.0-77956874627OAI: diva2:372969
QC 20101129Available from: 2010-11-29 Created: 2010-11-26 Last updated: 2012-03-21Bibliographically approved

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Tkachev, Vladimir
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Mathematics (Dept.)

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