On the DDVV conjecture and the comass in calibrated geometry. I

DOI10.1007/s00209-007-0281-6zbMath1180.53055arXivmath/0610709OpenAlexW2120738448WikidataQ122870679 ScholiaQ122870679MaRDI QIDQ943395

Timothy Choi, Zhiqin Lu

Publication date: 9 September 2008

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0610709

zbMATH Keywords

austere submanifoldcalibrated geometryDDVV conjecturecomass problem

Mathematics Subject Classification ID

Global submanifolds (53C40) Calibrations and calibrated geometries (53C38)

Related Items (23)

Pseudo-symmetries of generalized Wintgen ideal Lagrangian submanifolds ⋮ DDVV-type inequality for Hermitian matrices ⋮ The normal Ricci curvature inequality ⋮ On the generalized Wintgen inequality for submanifolds in complex and Sasakian space forms ⋮ On the generalized Wintgen inequality for Lagrangian submanifolds in complex space forms ⋮ Wintgen ideal submanifolds: new examples, frame sequence and Möbius homogeneous classification ⋮ Pseudosymmetry properties of generalised Wintgen ideal Legendrian submanifolds ⋮ A generalized Wintgen inequality for quaternionic CR-submanifolds ⋮ Variational formulas of higher order mean curvatures ⋮ Wintgen ideal submanifolds with vanishing Möbius form ⋮ The generalized Lu rigidity theorem for submanifolds with parallel mean curvature ⋮ Unnamed Item ⋮ Möbius geometry of three-dimensional Wintgen ideal submanifolds in \(\mathbb S^5\) ⋮ On some conjectures by Lu and Wenzel ⋮ Three special classes of Wintgen ideal submanifolds ⋮ Wintgen ideal submanifolds: reduction theorems and a coarse classification ⋮ Wintgen ideal submanifolds with a low-dimensional integrable distribution ⋮ Normal scalar curvature conjecture and its applications ⋮ Geometry of 6-dimensional Hermitian manifolds of the octave algebra ⋮ Almost contact metric structures on the hypersurface of almost Hermitian manifolds ⋮ CR-Submanifolds in Complex and Sasakian Space Forms ⋮ Generalized Wintgen inequality for Lagrangian submanifolds in quaternionic space forms ⋮ Some generalizations of the DDVV and BW inequalities

Cites Work

• Calibrated geometries
• Volume-minimizing cycles in Grassmann manifolds
• The stable 4-dimensional geometry of the real Grassmann manifolds
• Some remarks on the geometry of austere manifolds
• The Pontryagin 4-form
• Mean curvature and shape operator of isometric immersions in real-space-forms
• Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length
• A class of austere submanifolds
• Unnamed Item
• Unnamed Item
• Unnamed Item

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