Scalar curvature rigidity of certain symmetric spaces. (English) Zbl 0911.53032

Lalonde, François (ed.), Geometry, topology, and dynamics. Proceedings of the CRM workshop, Montreal, Canada, June 26–30, 1995. Providence, RI: American Mathematical Society. CRM Proc. Lect. Notes. 15, 127-136 (1998).
The author gives a survey of selected local and global rigidity conditions on Riemannian manifolds, with the former being primarily related to the proofs of the positive mass conjecture in general relativity. The exposition concerns seven results: four local theorems (two being due to the author) and three global theorems (one being a generalization of an unpublished 1991 result of M. Llarull to Hermitian symmetric spaces by the author).
The discussion of the material is informal and instructive, emphasizing methodology and motivation, and providing sketches rather than detailed proofs of the theorems. Unfortunately, only one of the author’s papers [M. Min-Oo, Math. Ann. 285, 527-539 (1989; Zbl 0686.53038)] on the results discussed in this survey has been published to date.
For the entire collection see [Zbl 0892.00044].


53C35 Differential geometry of symmetric spaces
83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
53C20 Global Riemannian geometry, including pinching


Zbl 0686.53038