Cosmetic composition containing a statistical polymer with a linear chain of ethylenic nature

Cosmetic method for reducing or treating age signs, comprising applying to the skin at least one composition comprising, in a physiologically acceptable medium, at least one statistical copolymer with a linear main chain of ethylenic nature, in which the said copolymer:

• (i) has a weight-average molecular mass of between 15,000 and 600,000 g/mol,
• (ii) contains at least 70% of monomer units derived from monomers whose homopolymers have a glass transition temperature of greater than 40° C.,
• (iii) also contains at least one “monomer unit” derived from an at least partially neutralized ionic hydrophilic monomer, and
• (iv) has an overall glass transition temperature of greater than or equal to 45° C.,
• and being in the form of a water-in-oil emulsion or a multiple emulsion, in an amount that is effective for smoothing out or effacing wrinkles and fine lines on human skin by means of a tensioning effect.