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We show that Veronese varieties of dimension n 4 do not carry any Ulrich bundles of rank r 3. In order to prove this, we prove that a Veronese embedding of a complete intersection of dimension m 4, which if m=4 is either P⁴ or has degree d 2 and is very general and not of type (2), (2, 2), does not carry any Ulrich bundles of rank r 3.
Lopez et al. (Wed,) studied this question.