Holomorphons and the standard almost complex structure on S^6

• Autorzy: Milewski J.
• Języki publikacji: EN

Abstrakty

EN

We consider Euler–Lagrange equations of families of nonnegative functionals defined on tensor fields of the type (1, 1), which are equal to zero only for complex structures tensor fields. As a solution of the equations we define the notion of holomorphon to distinguish a new class of tensor fields on Riemannian manifolds. Next, as our main result, we construct a holomorphon on the 6–dimensional sphere S^6.

Słowa kluczowe

EN

Riemannian geometry; almost complex structure; Nijenhuis tensor; variational principle

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2006
• Tom: Vol. 46, [Z] 2
• Strony: 245--254
• Opis fizyczny: bibliogr. 11 poz.

Twórcy

autor

Milewski J.

• Institute of Mathematics, Pozna´n University of Technology ul. Piotrowo 3A, 60-965 Pozna´n, Poland,

Bibliografia

• [1] A. Newlander and L. Nirenberg, Complex analytic coordinates in almost complex manifolds, Ann. Mat. 65 (1957), 391-404.
• [2] S. Kobayashi and K. Nomizu, Foundations of differential geometry I, II, Interscience Publications, New York 1963, 1969.
• [3] C. LeBrun, Orthogonal complex structure on S6, Proc. Amer. Math. Soc. 101 (1987), 136-138.
• [4] M. Karoubi, K-Theory an introduction, Springer-Verlag 1978.
• [5] A. Gray, A property of a Hypothetical Complex Structure on the Six Sphere, Boll. Un. Mat. It. B7(11)(2) (1997), 251-255.
• [6] A. Marshakov, A. I. Niemi Yang-Mills, Complex Structures and Chern's Last Theorem, Mod. Phys. Lett. A20 (2005), 2583-2600.
• [7] A. Winterhalder, Linear Nijenhuis Tensors and the Construction of Integrable Systems, Freiburg Preprint THEP 97/16.
• [8] A. G. Kurosz, Lectures in General Algebra, GIFML, Moscow 1962 (in Russian).
• [9] L. D. Landau and E. M. Lifshitz Field Theory, Nauka, Moscow 1973 (in Russian). 254 Holomorphons and the standard almost complex structure on S6
• [10] B. S. DeWitt, Dynamical Theory of Groups and Fields, Gordon and Breach Science Publishers, New York 1965.
• [11] J. Milewski, Holomorphons, Grant PB-43-035/04 BW, Poznań University of Technology 2004.