The Gaussian curvature via the contact angle of immersed surfaces into the Euclidean three sphere

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The aim of this paper is to present a relation for the Gaussian curvature of an immersed surface M2 of the Euclidean sphere S3 which involves the contact angle. This allows us to conclude that its Gaussian is flat provided its contact angle is constant. Moreover, we deduce that the Clifford tori are the unique surfaces with constant mean curvature having such propriety.