Quadratic forms between spheres and the non-existence of sums of squares formulae

DOI10.1017/S0305004100066226zbMath0613.55009MaRDI QIDQ4720404

Paul Y. H. Yiu

Publication date: 1986

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

zbMATH Keywords

bilinear formsHopf constructionsums of squares formulas

Mathematics Subject Classification ID

Sphere bundles and vector bundles in algebraic topology (55R25) Homotopy groups of spheres (55Q40) General binary quadratic forms (11E16) Hopf invariants (55Q25)

Related Items (12)

Quadratic forms between Euclidean spheres ⋮ NEW CONSTRUCTIONS OF EIGENMAPS BETWEEN SPHERES ⋮ Geometry of normed bilinear maps and the 16-square problem ⋮ Compositions of hermitian forms ⋮ Harmonic morphisms and circle actions on 3- and 4-manifolds ⋮ Biharmonic homogeneous polynomial maps between spheres ⋮ Classification of quadratic harmonic maps of \(S^7\) into \(S^7\) ⋮ Non-existence of quadratic harmonic maps of $S^{4}$ into $S^{5}$ or $S^{6}$ ⋮ A note on the fundamental theorem of algebra for the octonions ⋮ Polynomial Harmonic Morphisms between Euclidean Spheres ⋮ Harmonic polynomial morphisms between Euclidean spaces ⋮ Circles and quadratic maps between spheres

Cites Work

• On the non-existence of elements of Hopf invariant one
• Some new results on composition of quadratic forms
• Orthogonal pairings of Euclidean spaces
• Dilatation phenomena in the homotopy groups of spheres
• Construction of nonsingular bilinear maps
• Immersing projective spaces
• Polynomial maps from spheres to spheres
• Über Richtungsfelder in den projektiven Räumen und einen Satz aus der reellen Algebra
• Ein topologischer Beitrag zur reellen Algebra
• THE GROUPS 7π(V_nm)(I)
• A series of monomial pairings
• Elements in the Stable Homotopy Groups of Spheres which are not Bilinearly Representable

This page was built for publication: Quadratic forms between spheres and the non-existence of sums of squares formulae