Kowalczyk, Daniel Isometric immersions into products of space forms. (English) Zbl 1213.53079 Geom. Dedicata 151, 1-8 (2011). The author proves the existence and uniqueness of an isometric immersion of a Riemannian manifold into the Riemannian product of two spaces forms, extending the result obtained by B. Daniel [Trans. Am. Math. Soc. 361, No. 12, 6255–6282 (2009; Zbl 1213.53075)]. Reviewer: Constantin Călin (Iaşi) Cited in 9 Documents MSC: 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) 53C40 Global submanifolds 53B25 Local submanifolds Keywords:isometric immersions; Riemannian product Citations:Zbl 1213.53075 PDFBibTeX XMLCite \textit{D. Kowalczyk}, Geom. Dedicata 151, 1--8 (2011; Zbl 1213.53079) Full Text: DOI References: [1] Daniel B.: Isometric immersions into $${\(\backslash\)mathbb{S}\^{n}\(\backslash\),\(\backslash\)times\(\backslash\),\(\backslash\)mathbb{R}\(\backslash\), {\(\backslash\)rm and}\(\backslash\), \(\backslash\)mathbb{H}\^{n} \(\backslash\),\(\backslash\)times\(\backslash\), \(\backslash\)mathbb{R}}$$ and applications to minimal surfaces. Trans. Am. Math. Soc. 361, 6255–6282 (2009) · Zbl 1213.53075 · doi:10.1090/S0002-9947-09-04555-3 [2] Dillen F.: Equivalence theorems in affine differential geometry. Geom. Dedicata 32, 81–92 (1989) · Zbl 0684.53012 · doi:10.1007/BF00181438 [3] Dillen F., Nomizu K., Vrancken L.: Conjugate connections and Radon’s theorem in affine differential geometry. Monatsh. Math. 109, 221–235 (1990) · Zbl 0712.53008 · doi:10.1007/BF01297762 [4] Lira, J.H., Tojeiro, R., Vitório, F.: A Bonnet theorem for isometric immersions into product of space forms (preprint) · Zbl 1208.53061 [5] Piccione P., Tausk D.: An existence theorem for G-strucure preserving affine immersions. Indiana Univ. Math. J. 57, 1431–1465 (2008) · Zbl 1163.53009 · doi:10.1512/iumj.2008.57.3281 [6] Yano, K., Kon, M.: Structures on manifolds, series in pure mathematics, 3. World Scientific Publishing Co. · Zbl 0557.53001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.