Chengjie YU . DE RHAM DECOMPOSITION FOR RIEMANNIAN MANIFOLDS WITH BOUNDARY^*[J]. Acta mathematica scientia, Series B, 2023 , 43(1) : 51 -62 . DOI: 10.1007/s10473-023-0104-9

[1] Ambrose W.Parallel translation of Riemannian curvature. Ann of Math, 1956, 64(2): 337-363
[2] Blumenthal R A, Hebda J J.The generalized Cartan-Ambrose-Hicks theorem. C R Acad Sci Paris Sér I Math, 1987, 305(14): 647-651
[3] Cartan É.Leçcons sur la Géométrie des Espaces de Riemann. 2nd ed. Paris: Gauthier-Villars, 1946 (French)
[4] Chen Zhiqi.The uniqueness in the de Rham-Wu decomposition. J Geom Anal, 25 2015, 4: 2687-2697
[5] de Rham Georges. Sur la reductibilité d’un espace de Riemann. Comment Math Helv, 1952, 26: 328-344 (French)
[6] Eschenburg J -H, Heintze E.Unique decomposition of Riemannian manifolds. Proc Amer Math Soc, 1998, 126(10): 3075-3078
[7] Foertsch T, Lytchak A.The de Rham decomposition theorem for metric spaces. Geom Funct Anal, 2008, 18(1): 120-143
[8] Hicks N.A theorem on affine connexions. Illinois J Math, 1959, (3): 242-254
[9] Klingenberg Wilhelm P A. Riemannian Geometry. De Gruyter Studies in Mathematics, 1. 2nd ed. Berlin: Walter de Gruyter & Co, 1995
[10] Joyce D.On manifolds with corners//Advances in Geometric Analysis. Adv Lect Math 21. Somerville, MA: Int Press, 2012
[11] Kobayashi S, Nomizu K.Foundations of Differential Geometry. Vol I. Reprint of the 1963 original. Wiley Classics Library. A Wiley-Interscience Publication. New York: John Wiley & Sons, Inc, 1996
[12] Maltz R.The de Rham product decomposition. J Differential Geometry, 1972, 7: 161-174
[13] O’Neill B. Construction of Riemannian coverings. Proc Amer Math Soc, 1968, 19: 1278-1282
[14] Shi Yongjie, Yu Chengjie.Rigidity of a trace estimate for Steklov eigenvalues. J Differential Equations, 2021, 278: 50-59
[15] Warner Frank W.Foundations of Differentiable manifolds and Lie Groups. Corrected reprint of the 1971 edition. Graduate Texts in Mathematics, 94. New York, Berlin: Springer-Verlag, 1983
[16] Wu H.On the de Rham decomposition theorem. Illinois J Math, 1964, 8: 291-311
[17] Yu Chengjie.Fundamental theorem for submanifolds in general ambient spaces. Preprint