Let S be a regular surface endowed with a very ample line bundle \(\mathcal O_S(h_S)\). Taking inspiration from a very recent result by D. Faenzi on K3 surfaces, we prove that if \({\mathcal O}_S(h_S)\) satisfies a short list of technical conditions, then such a polarized surface supports special Ulrich bundles of rank 2. As applications, we deal with general embeddings of regular surfaces, pluricanonically embedded regular surfaces and some properly elliptic surfaces of low degree in \(\mathbb {P}^{N}\). Finally, we also discuss about the size of the families of Ulrich bundles on S and we inspect the existence of special Ulrich bundles on surfaces of low degree.

令S为具有非常丰富的线束\（\ mathcal O_S（h_S）\）的规则曲面。从D. Faenzi最近在K 3曲面上获得的结果中汲取灵感，我们证明如果\（{\ mathcal O} _S（h_S）\）满足一小段技术条件，那么这样的极化表面将支持特殊的Ulrich束在应用程序中，我们处理\（\ mathbb {P} ^ {N} \）中的常规曲面的一般嵌入，在深层中嵌入的规则填充的常规曲面和一些适当的低度椭圆形曲面。最后，我们还讨论了S上Ulrich束的族的大小，并检查了低度表面上特殊Ulrich束的存在。