The notion of two-numbers of connected Riemannian manifolds was introduced about 35 years ago in [Un invariant geometrique riemannien, C. R. Acad. Sci. Paris Math. 295 (1982), 389--391] by B.-Y. Chen and T. Nagano. Later, two-numbers have been studied by a number of mathematicians and it was then proved that two-numbers related closely with several important areas in mathematics. The main purpose of this article is to survey on two-numbers and their applications. At the end of this survey, we present several open problems and conjectures on two-numbers.
"Two-numbers and their applications - A survey." Bull. Belg. Math. Soc. Simon Stevin 25 (4) 565 - 596, december 2018. https://doi.org/10.36045/bbms/1546570911